SENSITIVITY ANALYSIS OF THE SECONDARY HEAT BALANCE AT ...

SENSITIVITY ANALYSIS OF THE SECONDARY HEAT BALANCE

AT KOEBERG NUCLEAR POWER STATION

by

Haydn Boyes

Dissertation presented for the Masters degree in Engineering: Nuclear Power

Department of Electrical Engineering Faculty of Engineering and the Built Environment

University of Cape Town

December 2020

Cape Town South Africa

Universi

ty of

Cape T

own

The copyright of this thesis vests in the author. No quotation from it or information derived from it is to be published without full acknowledgement of the source. The thesis is to be used for private study or non-commercial research purposes only.

Published by the University of Cape Town (UCT) in terms of the non-exclusive license granted to UCT by the author.

Universi

ty of

Cape T

own

1

ABSTRACT

At Koeberg Nuclear Power Station, the reactor thermal power limit is one of the most important quantities specified in the operating licence, which is issued to Eskom by the National Nuclear Regulator (NNR). The reactor thermal power is measured using different methodologies, with the most important being the Secondary Heat Balance (SHB) test which has been programmed within the central Koeberg computer and data processing system (KIT). Improved accuracy in the SHB will result in a more accurate representation of the thermal power generated in the core. The input variables have a significant role to play in determining the accuracy of the measured power. The main aim of this thesis is to evaluate the sensitivity of the SHB to the changes in all input variables that are important in the determination of the reactor power. The guidance provided by the Electric Power Research institute (EPRI) is used to determine the sensitivity. To aid with the analysis, the SHB test was duplicated using alternate software. Microsoft Excel VBA and Python were used. This allowed the inputs to be altered so that the sensitivity can be determined. The new inputs included the uncertainties and errors of the instrumentation and measurement systems. The results of these alternate programmes were compared with the official SHB programme. At any power station, thermal efficiency is essential to ensure that the power station can deliver the

maximum output power while operating as efficiently as possible. Electricity utilities assign

performance criteria to all their stations. At Koeberg, the thermal performance programme is

developed to optimize the plant steam cycle performance and focusses on the turbine system. This

thesis evaluates the thermal performance programme and turbine performance.

The Primary Heat Balance (PHB) test also measures reactor power but uses instrumentation within

the reactor core. Due to its location inside the reactor coolant system, the instrumentation used to

calculate the PHB is subject to large temperature fluctuations and therefore has an impact on its

reliability. To quantify the effects of these fluctuations, the sensitivity of the PHB was determined.

The same principle, which was used for the SHB sensitivity analysis, was applied to the PHB. The

impact of each instrument on the PHB test result was analysed using MS Excel. The use of the

software could be useful in troubleshooting defects in the instrumentation.

A sample of previously authorised tests and associated data were used in this thesis. The data for

these tests are available from the Koeberg central computer and data processing system.

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ACKNOWLEDGEMENTS

I would like to thank my academic supervisor, Professor Tunde Bello-Ochende, for his guidance,

support and encouragement throughout the duration of the programme. It has been a great

privilege working with him. I would also like to thank my industrial supervisor, Mr Nazier Allie for his

time and all the information which he shared with me. I am also thankful to Mr Luqmaan Salie for his

help regarding the Thermal Energy Programme. Finally, I thank my family for their patience as well

as their never-ending support and love.

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DECLARATION

I know the meaning of plagiarism and declare that all the work in the document, save for that

which is properly acknowledged, is my own. This thesis/dissertation has been submitted to the

Turnitin module (or equivalent similarity and originality checking software) and I confirm that

my supervisor has seen my report and any concerns revealed by such have been resolved with

my supervisor.

Haydn Boyes

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TABLE OF CONTENTS Abstract 1 Acknowledgements 2 Declaration 3 Table of contents 4 List of figures 6 List of tables 7 Nomenclature 8 Abbreviations 9 Chapter 1: Introduction 10

1.1 Plant Operation 10 1.2 Primary Heat Balance (PHB) 10 1.3 Nuclear Flux Instrumentation System (RPN) 11 1.4 Secondary Heat Balance (SHB) 11

1.5 Steam Generator Design 11 1.6 Calculation of Thermal Power 12 1.7 Problem Statement 12

1.8 Objectives 13 1.9 Scope and Limitations 13 1.10 Organisation of the Report 14

Chapter 2: Literature Review 15

2.1 Thermal Performance Programme 15 2.2 SHB at Koeberg 15 2.3 SHB at Other Nuclear Power Plants (NPPS) 15 2.4 Instrumentation Accuracy 17 2.5 International Standards 20 2.6 Statistical Analysis 20

Chapter 3: Control Volume Energy Balance of the Turbine Cycle

3.1 Thermal Performance Programme (TPP) 21 3.2 Turbine Performance 23 3.3 Conclusion 24

Chapter 4: Energy Balance of the Reactor

4.1 Background 25 4.2 Secondary Heat Balance 26 4.3 Independent Verification of the Manual Calculations 30 4.4 Compilation of SHB Using Alternate Coding Systems 31 4.5 SHB Accuracy 33 4.6 Conclusion 33

Chapter 5: Analysis of SHB Sensitivity to Instrumentation Accuracy

5.1. Accuracy of the Measurement System 34 5.2 Feedwater Flow Uncertainty 34 5.3 Random or Precision Error 39 5.4 Influence Factor / Sensitivity 42 5.5 Error Analysis 43 5.6 Conclusion 44

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Chapter 6 Steam Generator Thermal Hydraulic Effects

6.1 Factors Affecting Performance in the Steam Generator 46 6.2 Recirculation Flow in the Steam Generator 47 6.3 Oscillations 47 6.4 Conclusion 49

Chapter 7: Primary Heat Balance

7.1 Measurement of PHB 50 7.2 PHB Uncertainty 54 7.3 PHB Sensitivity analysis 55 7.4 Reactor Coolant Pump 55 7.5 Conclusion 56

Chapter 8: Summary and recommendations 57 References 59 Appendix 1 62 Appendix 2 66 Appendix 3 71 Appendix 4 73 Appendix 5 74 Appendix 6 76 Appendix 7 77 Appendix 8 78 Appendix 9 80 Appendix 10 81 Appendix 11 83 Appendix 12 84 Appendix 13 87 Appendix 14 89 Appendix 15 90 Appendix 16 91 Appendix 17 92 Appendix 18 94 Appendix 19 96

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LIST OF FIGURES

Figure 1.1 Nuclear Power Plant Operation

Figure 1.2 Steam generator design

Figure 3.1 Schematic representing the secondary cycle

Figure 3.2 T-S diagram

Figure 4.1 Layout of the reactor Coolant system of a three loop PWR

Figure 4.2 Steam Generator

Figure 5.1 Linearity graph for SG1 Feedwater temperature sensor

Figure 6.1 Total average minus Average per period for SG Pressures

Figure 7.1 Spatial layout of the Reactor Coolant System

Figure 7.2 Loop layout of Reactor Coolant System. (courtesy - Eskom)

Figure 7.3 Snapshot of PHB report

Figure A3-1 SHB Report Part A

Figure A3-2 SHB Report Part B

Figure A17-1 Worksheet showing data imported from KIT

Figure A17-2 Average values from KIT used as SHB Inputs

Figure A17-3 Calculation of feedwater enthalpy using the add-in named “water97-v13”

Figure A17-4 The VBA code for the feedwater iterative calculation was compiled and used in the

worksheet

FigureA17-5 Screen shot of MS Excel Worksheet containing SHB calculations

Figure A18-1 The imported files for the various functions

Figure A18-2 The data retrieval from MS Excel

Figure A18-3 The calculations for feedwater

Figure A18-4 The outputs into MS Excel

Figure A19-1 The data imported to MS Excel from KIT

Figure A19-2 The MS Excel Worksheet with the PHB calculations

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LIST OF TABLES

Table 3.1 Baseline model for various power levels

Table 3.2 Manual calculations versus manufacturer specifications

Table 4.1 SHB measured inputs

Table 4.2 SHB results

Table 4.3 Comparison of results: Manual calculations versus SHB Programme

Table 4.4 Comparison of results: MS Excel VBA versus manual calculations and SHB

Programme for SG1

Table 5.1 List of instrumentation used in the SHB

Table 5.2 Linearity analysis and Calibration coefficients for SG1 Feedwater

Table 5.3 Summary of errors and uncertainties for FW temp sensors

Table 5.4 Total Uncertainty

Table 5.5 Sensitivity Analysis

Table7.1 PHB: Summary of results

Table7.2 Sensitivity analysis of loop

Table A2-1 SHB measured inputs

Table A2-2 SHB Manual calculations

Table A7-1 Systematic errors for SHB

Table A9-1 Random Uncertainties

Table A10-1 Sensitivity Analysis of SHB instruments

Table A10-2 Combining error and Sensitivity SHB instruments

Table A12-1 Summary of PHB results

Table A14-1 PHB instruments Systematic Errors

Table A14-2 PHB instruments combining Systematic Errors and Uncertainty

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NOMENCLATURE

T Temperature °C

P Pressure kPa

H Enthalpy kJ/kg

S Entropy kJ/kg.K

V Specific Volume m3/kg

Cp specific heat capacity JkgK

Q Flow m3/h

ṁ Mass flow kg/s

ρ Density kg/m3

K thermal conductivity W mK

λ expansion coefficient

η Dynamic Viscosity Pa.s

ΔP pressure difference kPa

Re Reynolds number

W Heat Energy MW

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ABBREVIATIONS

FW Feedwater

ISO International Organisation for standardisation

SHB Secondary Heat Balance

PHB Primary Heat Balance

KIT Computer and data processing System

EPRI Electric Power Research Institute

VBA Visual Basic for applications

KBG Koeberg Nuclear Power Station

RPN Nuclear Flux Instrumentation system

SG Steam Generator

APG Blowdown System

RTD Resistance Temperature Detector

SAR Safety Analysis Report

NRC National Regulatory Commission

USA United States of America

ANN Artificial Neural Networks

NPP Nuclear Power Plant

UT Ultrasonic

RCP Reactor Coolant System

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CHAPTER 1

INTRODUCTION

1.1 Plant Operation

At Koeberg Nuclear Power Station, the Reactor Coolant System (also called the primary system) is a

three loop system and each loop consists of a common reactor vessel and pressurizer with separate

steam generators and reactor coolant pumps. The primary function of the reactor coolant system is

to transfer the heat from the fuel in the reactor vessel to the steam generators. Refer to Fig 1

The turbine cycle or secondary system consists of the turbine, generator, condenser, feedwater

heaters and pumps as well as all other components that assist in improving the system efficiency such

as reheaters, steam drains etc. The secondary system is not in direct contact with the primary system

and obtains its energy via the steam generators. The steam generator is a vertical, shell and tube heat

exchanger, with primary water on the tube side. Enthalpy changes in the secondary water in the steam

generator are based on the temperature of the feedwater and the properties of the exiting saturated

steam.

1.2 Primary Heat Balance (PHB)

The reactor power is measured by using in-core instrumentation. The instrumentation used to

calculate the PHB is subject to large temperature fluctuations and as a result, the PHB is not as

accurate as other measurement systems.

Reactor Coolant System (Primary System) Turbine Cycle (Secondary System)

Figure 1.1: Nuclear Power Plant Operation

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1.3 Nuclear Flux Instrumentation System (RPN)

The reactor power can be measured by measuring the neutron flux, which is proportional to reactor

power. Neutron detectors are placed outside the reactor pressure vessel. The detectors then measure

the neutron flux leakage, which in turn is proportional to the neutron flux inside the reactor. Thus, by

measuring the neutron flux leakage, it is possible to measure the power generated by the reactor. The

detectors are used for control and protection functions. The bombardment of neutrons from the core

on the detectors affects its accuracy and causes the readings to drift over time, requiring frequent

calibration.

1.4 Secondary Heat Balance (SHB)

The Secondary Heat Balance is an energy balance across the steam generators, which are shell and U-

tube type heat exchangers used to transfer the heat from the reactor to the turbine. The SHB uses

sensors located on the secondary side of the steam generators and therefore are not subject to the

large temperature fluctuations and neutronic disturbances that affect the PHB and RPN.

Figure 1.2: Steam generator design

1.5 Steam Generator (SG) Design

The steam generator (see figure 1.2) is a vertical shell and U-tube heat exchanger with integral

moisture separating and drying equipment. The reactor coolant flows through the inverted U-tubes,

entering and leaving through nozzles located in the hemispherical bottom or channel head, also called

lower head or water box, which is divided into inlet and outlet chambers by a vertical partition plate.

Feedwater flows into the steam generator through the nozzle located in the upper head of the SG. It

is distributed by means of the feedwater ring through inverted J-tubes, welded to the upper section

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of the feedwater ring. Steam is generated on the secondary side and flows upward past the tube

bundle. It then flows through the moisture separator and chevron driers to the outlet nozzle at the

top of the vessel. The tube sheet is a thick metal plate at the bottom of the SG, between the primary

water boxes and the tube bundles. Two blowdown pipes are situated just above the main tubeplate

to drain the liquid along with solid deposits which collect in this area. This blowdown system is

beneficial for health of the SG, by eliminating impurities and reducing sludge buildup.

1.6 Calculation of thermal power

The thermal power of the reactor is determined from the enthalpy balance for each steam generator.

Koeberg is a three loop PWR.

𝑊𝑅 = 𝑊𝑆𝐺1 + 𝑊𝑆𝐺2 + 𝑊𝑆𝐺3 − 𝑊∆𝑃𝑅 (1.1)

WR = Thermal power of reactor

WSG1 = Thermal power of steam generator 1

WΔPR = Thermal power added to the primary circuit by primary components.

The thermal power of one steam generator is:

𝑊𝑆𝐺 = ℎ𝑉 (𝑄𝐸 − 𝑄𝑃) + ℎ𝑃𝑄𝑃 − ℎ𝐸𝑄𝐸 (1.2)

Where:

hP = Blowdown enthalpy

hE = Feedwater enthalpy

QP = Blowdown flowrate

QE = Feedwater flowrate

hV = Steam enthalpy,

These calculations are the basics of the enthalpy balance across the SGs. Further calculations

(Appendix 2) will be performed to determine the feedwater densities, flow coefficients, etc.

1.7 Problem statement

Improved accuracies in the Secondary Heat Balance will result in a more accurate representation of

the thermal power generated in the core. The input variables have a significant role to play in

determining the accuracy of the measured power. Due to the dynamic thermal hydraulic

characteristics of the secondary system, it is essential to understand the factors that affect each input

variable measured by the instrumentation. The data acquisition system also affects the variable and

performs an important function in producing highly accurate information. It is therefore vital that the

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quality of the data is not compromised during the process, when converting the recorded parameters

into a digital format. Furthermore, the secondary system is interdependent on the primary system,

which has unique thermal hydraulic properties. Considering that this test produces a result which is

important to nuclear safety and vital for Koeberg’s operating mandate as per the licence, it is prudent

to understand the factors that could influence the measurement of reactor power. Once the factors

are well understood, it will allow for the optimisation of output power, thereby providing the

maximum amount of power to the transmission network for use by the general public.

Although the reactor power is measured by other systems besides the SHB i.e. the Primary Heat

Balance (PHB) and Nuclear Flux Instrumentation System (RPN), the SHB uses sensors located on the

secondary side of the steam generators and therefore are not subject to the large temperature

fluctuations and neutronic disturbances that affect the PHB and RPN. These systems are calibrated

using the SHB and therefore the inaccuracies associated with the SHB must be clearly understood.

The source code for the original Secondary Heat Balance content was written in ANSI Fortran 77, which

is a very old programming code. Since Fortran was developed in the 1980s, it has been superseded by

many programming codes. The version currently in use, is the KIT system which contains unique

algorithms within the data processing software to compute the thermal power. Due to the age and

obsolescence of the coding language, it is crucial that a newer software programme is used. Computer

technology has developed significantly over the years and outdated software creates major challenges

when newer hardware is purchased due to defects and failures.

The proposed research is to evaluate the sensitivity that the various inputs have on the Secondary

Heat Balance result and other external factors that could influence the outcome, originating either

from the secondary or primary systems. This will also aid in troubleshooting and predicting thermal

performance should any defects occur on either the instrumentation, primary or secondary systems.

1.8 Objectives

It is intended that the following objectives will be met with the research project:

Evaluate the current accuracy of the Secondary Heat Balance.

Assess each input variable that could affect the accuracy of the measured power.

Evaluate the data acquisition methodology and assess the factors which influence the

quality of the data.

Review the thermal hydraulic characteristics of the water and steam flow inside the steam

generator and how it can affect the measurements.

Review the Thermal Performance programme and its impact on the measurement of the

SHB. The research will however focus more on the primary system and the intent of this

section is to provide the context of the thermal balance across the steam generator.

Evaluate the accuracies in the PHB and perform a sensitivity analysis of the PHB.

The SHB software code will be re-written in Microsoft Excel VBA and Python.

1.9 Scope and Limitations

The research focusses on the Secondary Heat Balance and Primary Heat Balance methods used at

Koeberg Nuclear Power Station which is a three loop Pressurised Water Reactor (PWR). There are

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various methods being used at other power stations in the world to measure reactor power. While

many of the stations use a similar method as Koeberg, the assumptions and data used in this report

is unique to Koeberg.

1.10 Organisation of the Report

Chapter 1 contains an introduction to the research

Chapter 2 contains the literature review with previous work done on instrumentation accuracy and

sensitivity for nuclear plants. Various international standards and position papers are reviewed to

ensure the methodology used in the report is in line with international norms.

Chapter 3 contains the details of the Thermal Performance Programme and the method used when

calculating the energy balance of the turbine cycle. Even though the Thermal Performance

Programme (TPP) is separate from the reactor thermal power programme, it shows how the heat

energy from the reactor is used in the turbine cycle.

Chapter 4 shows how the energy balance across the reactor is determined using the Secondary Heat

Balance method.

Chapter 5 evaluates the sensitivity of the Secondary Heat Balance to the instrumentation accuracy.

It includes various uncertainties and shows the impact on the SHB result.

Chapter 6 looks at the thermal hydraulic effects of the steam generator and the factors that affect

the performance of the steam generator. The Secondary Heat Balance test is reviewed by taking in

to account these factors and the results are shown.

Chapter 7 provides details of how the PHB is determined and the uncertainties associated with it.

Chapter 8 contains information on the newly developed software programmes.

Chapter 9 contains conclusions based on the discussion, followed by recommendations.

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CHAPTER 2

LITERATURE REVIEW

2.1 Thermal Performance Programme

This programme is intended to maximize unit generator output and optimize plant steam cycle

thermal performance under steady state operation while at full power. The programme focuses on

turbine performance, efficient operation of the main steam, extraction steam, condensate, heater

drains, feed water, and condenser cooling water systems; feed water performance; condenser

performance and main generator power metering. While this programme directly interfaces with the

core thermal power calculation (SHB/PHB), station service loads and equipment reliability, the

administration and control of these technical areas is outside the scope of the thermal performance

programme (Salie, 2019). Therefore, the thermal performance programme does not directly address

core power calculations or system/component reliability monitoring.

2.2 SHB at Koeberg

The core thermal power is controlled by the operator based on the indications from the on-line

(KIT/Ovation) PHB and RPN (ex-core detectors) systems. These indicators are calibrated using the SHB,

which is the most accurate representation of core thermal power. An assessment for the need to

calibrate the PHB and RPN is performed once a week. Although the SHB is a live, on-line system and

provides real time information about the core power, this information cannot be used at random for

calibrating the PHB and RPN channels. To use the SHB for calibration purposes, the operator has to

ensure that during a selected time window the plant is operating in a stable state (Salie, 2013). The

stable state is assessed by the SHB software on KIT and endorsed by the operator. If this has been the

case, then the operator can generate the SHB test. To ensure further processing of the SHB test, the

operator must state that no interventions have been performed that could affect the SHB test result,

e.g. no dilution of the reactor, that could affect the power generated, has taken place over the SHB

test time window. If the SHB is determined to be accurate then it will be authorised for use to calibrate

the PHB and RPN.

At Koeberg, the PHB is averaged over 1 min and is used to determine whether the maximum core

thermal power has been exceeded. The alarm setpoint is set at 100% Pn which equates to 2775 MW.

When the PHB has drifted to more than 0.4% of the SHB measured value, it requires calibration

because the PHB will be indicating a core thermal power that is greater than the actual value (Maroka,

2015). It is important to note that this does not mean that the PHB will at all times indicate a value

greater than the SHB. Due to various parameters used in the calculation of the PHB, such as loop

temperatures, RCP pump speeds, grid frequency and loop flow rates, it is very possible for this

bias/offset to diminish or increase. The same goes for the SHB input parameters. The reason for the

conservative calibration of the PHB is to prevent overpowering events. Koeberg is licensed to produce

a maximum power of 2775 MWth and is not allowed to exceed this power level. With the PHB

calibrated conservatively, this ensures no overpowering. The accuracy differences between the PHB

and SHB will be valuable for later use.

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2.3 SHB at other Nuclear Power Plants (NPPs)

Exelon Generation Company, based in the United States of America (USA) performed a calculation to

determine the reactor core thermal power uncertainty. The purpose of this calculation was to

determine the uncertainty of the calculation performed by the Plant Process Computer (PPC), similar

to the SHB at Koeberg. By assessing the various instrument channel loop uncertainties, the total

uncertainty could be calculated using the reactor heat balance relationship. It was found that the total

uncertainty is 0.347 % of rated reactor thermal power. As per the nuclear regulator in the USA, the

National Regulatory Commission (NRC) this uncertainty is considered acceptable because it is within

the specified limit of 2%. This research has assisted nuclear plant owners to justify a smaller margin

for power measurement uncertainty. This is usually associated with highly accurate feedwater flow

measurement instrumentation that replaced older, less accurate instrumentation. The South African

National Nuclear Regulator has also authorised a 2% error for power measurements, which is the

threshold that is used for the sensitivity analysis in this thesis.

In another study, M. Jabbari et al. (2014) analysed the thermal power of a Russian VVER-1000 reactor

by using the secondary heat balance procedure and compared it with other methods such as the in-

core and ex-core neutron flux (power) monitoring systems. The calculated values of the reactor

thermal power by the SHB method used in his research are comparable with the reactor power

measured by the in-core and out-core instruments. In this study the SHB shows a smaller error in

comparison with the other methods utilizing the neutron detectors. These detectors are widely used

for reactor power measurement and are similar to the detectors used at Koeberg. These devices

incorporate a material chosen for its relatively high cross section for neutron capture leading to

subsequent beta or gamma decay. In its simplest form, the detector operates on directly measuring

the beta decay current following capture of the neutrons. Compared to the stability of the SHB

method, the neutron detectors are exposed to the continuous bombardment of neutrons from the

core which affects its accuracy and causes the readings to drift over time.

In their research, Mesquita et al (2014) aimed to develop new methodologies for on-line monitoring

of nuclear reactor power using other reliable processes besides neutron detectors. One method

proposed is the temperature difference between an instrumented fuel element and the pool water

below the reactor core. Another method consists of the steady-state energy balance of the primary

and secondary reactor cooling loops. A third method is the calorimetric procedure whereby a constant

reactor power is monitored as a function of the rate in temperature rise and the system heat capacity.

These procedures, fuel temperature, energy balance and calorimetric were implemented in the IPR-

R1 TRIGA nuclear research reactor at Belo Horizonte (Brazil) and has become the standard

methodology used for the reactor power measurement. With an uncertainty of 4%, the method was

proven to be fairly accurate and do not differ significantly from those obtained from conventional

nuclear measuring channels using neutron flux. The uncertainty of the SHB method used at Koeberg

will be compared to the 4% uncertainty of these methods.

2.4 Instrumentation accuracy

According to the International Atomic Energy Agency (IAEA, 2007), Online monitoring (OLM), involves

comparing the steady state output of each channel with its process parameter to assess the deviation

of the monitored value from the calculated value of the process variable. This is similar to the first

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step in traditional calibration methods. Each channel’s deviation from its measured parameter

represents its variation from the estimated value of the process. The amount of this variation is

compared with pre-established acceptance criteria. The acceptance criteria are used to determine

instrument performance and operability. Calculations for the acceptance criteria should be done in a

manner consistent with the plant assumptions. The SHB should therefore be evaluated against the

design assumptions of the plant. In the nuclear industry, the design is based on a worst case accident.

It should be demonstrated that the SHB will at all times comply with the design basis. The SHB utilises

a transient function that continually monitors deviations in the data from predetermined values.

With traditional calibration methods, instruments remain unattended for long periods. The possibility

therefore exists that certain types of instrument failures may remain undetectable. It is therefore

important to have the ability to re-analyse the test results if the calibrations show that the instruments

were out of tolerance while in use. This is to show that the previous tests met the design assumptions

through the full range of measurements.

At the Halden Reactor Project (Ruan D et al. 2002), they investigated available techniques aimed at

enhancing the accuracy of flow measurements, and reducing the measurement uncertainty. It was

found that in order to better estimate the feedwater flow, an integration of artificial neural networks

(ANNs) and cross-correlation analysis can be beneficial. The idea is to develop a “virtual flow meter"

based on neural cross-correlation of signals obtained from sensor pairs placed at spatially separated

locations along the feedwater pipe. Inputs to the neural virtual flow meter will also include other plant

measurements that have an influence on the velocity profile of the fluid in the pipe, e.g., temperature

and pressure measurements. These techniques were experimentally developed in a laboratory and is

intended to be used for a new type of sensor which will be able to provide better estimates of critical

process parameters. One of the main intentions of this project was to enhance the operators’ ability

in identifying and rectifying problems that affect the thermal performance of nuclear plants and assess

various computational intelligence approaches to flow measurements in NPPs.

Traditionally, due to limitations in technology, safety analysis of nuclear power plants were done by

using conservative models and resulted in the overdesign of components and systems. In recent years,

thanks to the accuracy of computational tools, safety analysis can be performed by using simulations

which are more realistic of actual plant conditions. There are however, some uncertainties associated

with these simulations and therefore these must be quantified. According to Gonzales (2018), the

source of the uncertainties can be either the input parameter or the nuclear reactions (i.e reactivity)

or thermo-hydraulic effects, all of which can affect the output. The research paper reviews the

simulation tools SEANAP and COBAYA4 to analyse the accuracy of the simulations. This is done by

interfacing with the physics and thermo-hydraulic codes as well as performing nodal analysis and

predictive sampling. The research shows that uncertainties were around 0.5% for the reactivity

simulations but increased to 7% if the reactor was unstable. It was found that the most significant

contributor to the uncertainty was the feedwater temperature because it had the most significant

effect on reactivity. The difference between this research and the uncertainty for the SHB, is that the

reactivity does not impact on the SHB output because it uses instrumentation located on the

secondary system and an increase (or decrease) in feedwater temperature will not significantly affect

the other parameters on the secondary system. The feedwater temperature however has a major

impact on reactivity in the primary system due to the moderator coefficient of the water.

In steam generators, special attention is given to preserving the boundary between the contaminated

water in the primary reactor coolant system and the water-steam mixture in the secondary system. It

is important for nuclear safety that these components are reliable and able to perform their function

in accident conditions. Results obtained by using simulation software RELAP5, developed for safety

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analyses of NPPs, showed that the steam generator design is able to effectively transfer heat in

accident conditions originating in the primary system or the secondary system (Sadek and Grgic 2017).

It is therefore important that thermal energy measurements across the steam generator reflects the

actual heat transfer so that the design assumptions are not challenged. This ensures that the steam

generator is not over stressed which could affect the performance of the steam generator in the event

of an accident.

One of the measurements which has a significant impact on SG thermal performance is the feedwater

flow. The thermal power in the SG is very sensitive to the feedwater flow. This feedwater passes

through the steam generator via a downcomer. The downcomer flow in SGs can provide unique fitness

for service and performance indicators related to overall thermo-hydraulic performance and safety

indicators. It highlights areas of degradation which is useful to the plant engineer, who can

recommend alterations. Janzen et al. (2014) reviews the benefits of downcomer-flow measurements

to nuclear power plant operators and describes methods that are commonly used. The research

summarizes the history and state-of-the-art of technology such as non-intrusive ultrasonic (UT)

systems as well as applications at nuclear power plants. These measurements can be used to

determine the existence of steam carry over, assess the effectiveness of steam-generator cleaning

and also provide useful information on transient/accident behaviour. In summary, the paper

concludes a 10% level of uncertainty as appropriate for UT flow measurements. The results also

suggest that the intrinsic accuracy of the UT measurements when optimized at room temperature

may be somewhat better than 10%. The best results show a relative error of ±8 %. Considering that

the SHB is sensitive to feedwater flow measurements, it is important to understand the impact that

the uncertainty of the feedwater flow will have on the thermal energy measurement. At Koeberg, an

orifice is used for feedwater flow measurements. The accuracy of the orifice will be compared against

UT flow measurements.

The increasing age of existing NPPs are forcing the global nuclear power industry to confront the

challenges of ageing in instrumentation. Temperature, humidity, radiation, electricity and vibration all

contribute to ageing and affects most instrument & control components. The traditional aging

management method is to replace equipment which requires the plant to be shut down. Recent

ageing management technologies, collectively known as online monitoring (OLM), enable plants to

monitor the condition and aging of their installed instrumentation while the plant is operating. OLM

techniques include low and high-frequency methods for noise analysis or methods based on

diagnostic sensors for vibration analysis or methods that inject a test signal into the component under

test. Hashemian, (2010) reviewed the various OLM methods and investigated possible improvements.

OLM emerged in the 1980s as a way to extend the intervals between calibrations of pressure

transmitters. In the 1990s, the nuclear industry adopted OLM techniques for equipment condition

monitoring. This included the monitoring of reactor internals, detecting leaks, verifying the thermal

performance of plants, measuring the stability of the reactor core, anticipating rotating equipment

failures, checking that valves are operating correctly and identifying loose parts within reactor

systems.

There are some OLM tools available for the protection of industrial monitoring systems against

measurement errors but not all industries utilize them. Madron et al. (2015) concentrated on the

protection of key results against systematic errors by using on‐line monitoring techniques. It was

found that errors can be hidden in flow measurements and in the properties of steam and water. The

research attempted to identify errors while ensuring accurate measurements and proposed a simple

19

method for OLM. This method is based on a linearization model and its success depends on the

magnitude of the deviation from the non-linear calibrations. For the SHB sensitivity analysis, a similar

method will be considered for the linearity analysis of the instrumentation.

The use of OLM methods for applications like monitoring the accuracy of pressure, level, and flow

transmitters has been formally approved by the U.S. and British regulatory authorities. The Sizewell B

plant in England anticipates significant savings per operating cycle when OLM technologies are fully

implemented. Because OLM methods are non-intrusive and in situ (the instrument is not removed

from the process), they can be used to monitor processes that are inaccessible while the plant is in-

service and avoid unnecessary maintenance to instrumentation that show no ageing issues. OLM is

making it easier to manage instrumentation ageing at NPPs. At Koeberg the SHB contains a watchdog

function which is similar to an OLM tool. It automatically verifies the data that is extracted from KIT to

ensure that data used in the SHB is accurate. This function will be evaluated.

2.5 International Standards

Nuclear Generation Group, Nuclear Engineering Standards (Vande Visse, 1997) provides the standard

for the Analysis of Instrument Channel Setpoint Error and Instrument loop accuracy. According to

them, the measurement process includes imperfections that causes errors in the test result. Errors

may be of two types, random or systematic. Random error results from unpredictable variations and

will be seen if there are repeated discrepancies in the measured parameter. Random errors of a

measurement cannot be compensated by correction. They can be minimized or reduced by increasing

the number of samples, increasing the accuracy of the instrument or by incorporating a measurement

procedure that reduces the sources of error. Similarly, systematic error also cannot be eliminated.

Systematic errors are from known sources and can be quantified. A correction factor may be applied

to the measurement result to compensate for this type of error. An error in the test result is not the

same as measurement uncertainty, and the two should not be confused. Both of these phenomena

are considered in this thesis.

The Electric Power Research institute compiled the Thermal Performance Engineering Handbook

(Mantey, 2013) where it provides guidance to thermal performance engineers when investigating the

cause of energy losses. It also proposes new ways to increase electric power output. This report

provides detailed descriptions of the components in the nuclear plant heat cycle and includes the

various errors associated with the instrumentation associated with power measurement.

The International Organization for Standardization (ISO) is a worldwide federation of national

standards bodies. ISO 5167 is a standard that specifies the requirements for measuring flows using

orifice plates. It covers the geometry, installation procedure and operating conditions of orifice plates

when they are used to measure the flowrate in a pipe. This setup is utilised in the SHB. It also gives

information for calculating the uncertainties that are associated with the configuration and

equipment. Because the SHB is very sensitive to the measurement of the feedwater flow, this standard

will be applied to the sensitivity analysis.

2.6 Statistical analysis

In order to quantify the uncertainty in instrumentation or systems, the analysis of the measured

parameter must show some variation. By using numerical simulation tools such as Computational Fluid

20

Dynamics (CFD), these uncertainties can be computed. Otgonbaatar (2016) determined the

uncertainty by using the normal probability distribution for the parameter which is measured. The

normal probability distribution is the probability that an instrument will produce a certain value based

on its manufactured accuracy. Additionally, a non-parametric formulation is used, which allows the

quantification and integration of uncertainties that are not expressed by the normal probability

distribution. As per the Wikipedia definition, “Non-parametric models differ from parametric models

in that the model structure is not specified but is instead determined from data. The term non-

parametric is not meant to imply that such models completely lack parameters but that the number

and nature of the parameters are flexible and not fixed in advance” This methodology was based on

the analysis of four industrial case studies where the measured parameters included mass flow rate,

steam generator recirculation ratio, cooling tower deformation and NOx emissions. The research

shows that these methods can be applied to all tests to express uncertainty. The methodology is

however extremely complex and the coding should be obtained for its use. Contributing to the

complexity is that the method must be used for each input parameter and the coding in CFD (eg Monte

Carlo method) has not been developed for the other measurements in the SHB and is therefore

beyond the scope of this thesis.

21

CHAPTER 3

CONTROL VOLUME ENERGY BALANCE OF THE TURBINE CYCLE

3.1 Thermal Performance Programme (TPP)

At any power station, thermal efficiency is essential to ensure that the power station can deliver the

maximum output power while operating as efficiently as possible. Electricity utilities assign

performance criteria to all their stations. At Koeberg the thermal performance programme is

developed to optimize the performance of the steam cycle. This cycle includes the turbines and all

steam systems linked to the turbine such as the extraction steam system, condensate system, heater

drains system and feed water heating system.

The Thermal Performance Programme (TPP) is separate from the reactor power programmes. The

measurement of the reactor thermal power is done using three different methodologies, namely the

Primary Heat Balance (PHB), the Reactor Neutron Protection System (RPN) and the Secondary Heat

Balance (SHB). Details of these were provided in Chapter 1. The difference between the TPP and the

SHB is that the TPP is focussed on the secondary systems of the plant to ensure that the turbine and

auxiliary systems perform as expected, whereas the SHB uses the secondary system parameters to

determine the primary system power. This thesis will focus more on the primary system and the intent

of this section is to provide the context of the thermal balance across the steam generator and how

the steam system is managed.

The TPP consists of five elements that provide a holistic view of the thermal performance. These

elements are necessary for the planning, execution and monitoring of a successful programme.

i. Baseline and modelling

Baseline values are required for key performance indicators. The baseline values are given

below in table 3.1.

Table 3.1: Baseline model for various power levels

The information in the table is from the turbine manufacture (Choquart, 2010), who also

provides the baseline values for enthalpy and entropy diagrams. The calculations performed

in this thesis are compared to the manufacturer supplied baseline values.

22

ii. Performance goals

The expected performance will differ at each station based on criteria set by the owner of the

plant. At Koeberg, these performance goals are defined by Eskom and documented in the

station performance contracts. Koeberg is accountable to the Eskom CEO on meeting these

targets.

iii. Monitoring and trending

Monitoring consists of periodic reviews of thermal performance data. This is determine if

current conditions are in line with expected targets. Monitoring is also used to verify the

effectiveness of corrective actions. Trending comprises of specific trends that show the critical

parameters which are used to ensure optimum thermal performance. Sufficient trending is

the backbone of a good thermal performance programme.

iv. Search and recovery

Search and recovery is an aspect of the programme that is used only when there is an

identified defect or deficiency in generation capacity. An investigation is initiated and specific

troubleshooting tools are implemented to identify the root cause. When the investigation is

concluded, it will specify a series of corrective actions which must be done to correct the

deficiency.

v. Communications/reporting

All the elements of the programme require certain documentation. All documentation are

kept for the life of the station and are subject to audits by the Quality Assurance

department.

3.2 Turbine Performance

The turbine consists of a double flow high pressure (HP) cylinder and three double flow low pressure

(LP) cylinders. From the SG, the main steam flows to the HP cylinder of the turbine. Inside the HP

cylinder, steam is divided into two equal flows, each going through seven expansion stages. The

expanded steam flows into reheaters before entering the three LP cylinders. Immediately after

entering each LP cylinder, the steam flows through seven expansion stages and is exhausted into the

condenser.

The turbine main steam system is a system of pipe-work and valves that is used to convey steam from

the steam generator to the high-pressure and low-pressure cylinders of the main turbine. The route

is described in three stages (refer to Figure 3.1):

convey saturated steam from the SG to the turbine high-pressure cylinder (7),

convey wet steam from the exhaust of the high-pressure cylinder to the Moisture Separator

Reheater (8),

convey superheated steam from the moisture separator re-heaters to the low-pressure

cylinders of the turbine (9).

In addition to the main flow-path through the turbine, the steam system also supplies steam to various

secondary consumers. We will not cover all the other steam flow paths in this thesis. What is

important here, are the main processes, which are covered. Figure 3.1 is a simplified diagram of the

cycle at Koeberg. The turbine reheat and feedwater systems are more complex than shown below but

23

Figure 3.1 is used as an illustration of the main steam system. Turbine performance is not the main

focus of this thesis and therefore various processes have been simplified to show only certain

components and the entry and exit enthalpies at those components (refer to Appendix 1). For

example, at Koeberg, there are fourteen feedwater heaters but the diagram below only shows two.

These two heaters represent the heat produced by all the other feedwater heaters. Key

measurements were taken at the points indicated below to obtain the enthalpy values and the

schematic represents the position of measured points. See figure 3.2 below. The analysis performed

in Appendix 1 is compared with the data provided by the manufacturer of the turbine.

Figure 3.1: Schematic representing the secondary cycle

Figure 3.2: T-S diagram

24

Using actual plant, the Enthalpy at each point was calculated and compared to the manufacturer’s

specifications to determine current performance versus expected performance. The energy

distribution within the Rankine cycle is clearly shown in the results. The results are shown below in

Table 3.2. The manufacturer values (Alstom, 2010) can be found in Appendix 1.

Enthalpy (kJ/kg) Difference (%)

At point Manual Calculation

Manufacturer supplied value

1 124.68 Not given N/A

2 128.7 131.1 -1.83

3 767.7 770.0 -0.29

4 771.5 774.2 -0.34

5 948.3 949.2 -0.09

6 948.3 Not given

7 2790.1 2792.9 -0.10

8 2513.6 2582 -2.64

9 2923 2924.3 -0.04

10 2092.4 2210.8 -5.35

Average difference -1.34

Table 3.2: Manual calculations versus manufacturer specifications

3.3 Conclusion

Thermal efficiency is essential to ensure that the power station can deliver the maximum output

power while operating as efficiently as possible. The Thermal Performance Programme is focussed on

the secondary systems of the plant to ensure that the turbine and auxiliary systems perform as

expected. The TPP consists of five elements that provide a holistic view of the thermal performance

of the plant. These include baseline modelling, performance goals, monitoring, search/recovery and

reporting.

Manual calculations were performed to determine the energy balance at various stages within the

cycle. These values were compared with the manufacturer supplied data. The average difference

between the two was found to be -1.3 %. With a small difference like this, the data from the manual

calculations can therefore be used for the development of other programmes. In Chapter 4 it will be

seen how the manual calculations of the SHB can be used to develop Excel and Python programmes.

These would be especially useful for fault finding troubleshooting within the cycle. For example, the

input parameters for any of the feedwater heaters can be used to determine if the heater is producing

the expected output energy. If not, then corrective actions can be developed to re-establish the

expected performance.

25

CHAPTER 4

ENERGY BALANCE OF THE REACTOR

4.1 Background

The Reactor Coolant System (also called the primary system) consists of the reactor vessel, the steam

generators, the reactor coolant pumps, a pressurizer, and the connecting piping (Eskom, 2019). A

reactor coolant loop contains a reactor coolant pump, a steam generator and the piping that connects

these components to the reactor vessel. The primary function of the reactor coolant system is to

transfer the heat from the fuel to the steam generators which then converts the feedwater to steam.

Fig 4.1: Layout of the reactor Coolant system of a three loop PWR (Courtesy of Eskom)

4.2 Secondary Heat Balance

The thermal power of the reactor is determined from the enthalpy balance for each steam generator

(Salie, 2013 ; Maroka, 2015).

𝑊𝑅 = 𝑊𝑆𝐺1 + 𝑊𝑆𝐺2 + 𝑊𝑆𝐺3 − 𝑊∆𝑃𝑅 (4.1)

Where:

WR = Thermal power of reactor

WSG1 = Thermal power of steam generator 1

WΔPR = Thermal power added to the primary circuit by primary components.



26

Where:

hV = Steam enthalpy,

hE = Feedwater enthalpy


hP = Blowdown enthalpy Blowdown is the extraction of impurities from the tubesheet. This is done by allowing some feedwater to be extracted from a bleed off pipe located just above the tubesheet.

QP = Blowdown flowrate

Fig 4.2: Steam Generator

The information used in this research was collected from actual plant data at Koeberg. The information

was recorded from Reactor no. 2 (Unit 2) on 10 January 2020 at 23:59.

When these values were recorded, the reactor was at 100% power. The values used earlier in this

thesis to calculate the thermal balance of the turbine, was at a similar plant state. The calculations

based on Rawoot, 2015 is shown in Appendix 2. The measured inputs are shown below in Table 4.1.

These values were used to perform the energy balance in the Secondary Heat Balance Equation.

Table 4.1: SHB measured inputs

Parameter SG1 SG2 SG3

Feedwater Pressure (kPa) 5382.19 5382.19 5382.19

Feedwater Temp (°C) 220.39 220.34 220.43

Blowdown Flow (kg/s) 3.77 3.77 3.77

Steam Pressure (kPa) 5004.0 5005.4 5015.7

Steam Temp (°C) 263 .1 264.4 265.3

Steam quality 0.9975 0.9975 0.9975

Blowdown

27

4.2.1 Steam Enthalpy at SG1 outlet (hv)

The steam is wet saturated vapour (by interpolation):

hv = hf + x hfg (4.1)

Where:

hf = saturated enthalpy

hfg = Enthalpy difference

x = dryness fraction (refer to Safety Analysis report II-3.3.3.1.1

s6 = sf + x sfg (4.2)

Where:

sf = saturated liquid Entropy

sfg = Entropy difference

4.2.2 Feedwater Enthalpy at SG1 inlet (hE )

Feedwater enthalpy is saturated liquid and found by interpolation

4.2.3 Feedwater Flowrate at SG1 inlet (QE)

Feedwater flowrate is measured using a differential pressure transmitter fitted across an orifice plate

which is located in the feedwater pipeline. The feedwater mass flowrate is the dominant factor in

determining the power output for the steam generator. Slight changes in this parameter will influence

the outcome significantly and therefore a lot of focus will be given to this parameter (Electricite de

France, 2001). The sensitivity of the various elements in the feedwater flowrate equation will be

evaluated later in this thesis.

As a guideline, the ISO Standard ISO 5167, 2003 was used for the calculation. This standard was

adopted by the various utilities across the world. Koeberg was constructed by a French consortium

and the French national utility EDF has also adopted the ISO standard for feedwater calculations.

𝑄𝐸 = 𝛼휀𝜋𝑑2

4√(2. ∆𝑃. 𝜌 (4.3)

Where:

α = Flow coefficient

ε = Expansion coefficient = 1 for incompressible fluids

d = diameter of orifice

ΔP = Differential pressure across orifice plate

ρ= Density of feedwater

28

4.2.4 Diameter of orifice (d)

Due to high temperatures the diameter of the orifice will change due to thermal expansion. A fixed

expansion coefficient for stainless steel is used.

d = d0 (1+λd(tE – td0) (4.4)

Where:

d0 = measured diameter at room temp = 257,5 mm

λd = expansion coefficient for Stainless steel = 0,000019

tE = Feedwater temperature

td0= room temperature = 23 °C

4.2.5 Inner diameter of pipe (D)

D = D0 (1+λD(tE – tD0) (4.5)

Where:

D0 = measured diameter at room temp = 369,4 mm

λD = expansion coefficient for Carbon steel = 0,0000128



4.2.6 Diameter ratio ( β)

𝛽 = 𝑑

𝐷 (4.6)

4.2.7 Feedwater density (ρ)

At 220,3 °C

𝐷𝑒𝑛𝑠𝑖𝑡𝑦, 𝜌 = 𝑚𝑎𝑠𝑠

𝑉𝑜𝑙𝑢𝑚𝑒 (4.7)

4.2.8 Flow coefficient (α)

𝛼 = 𝐴 + 𝐵. √106

𝑅𝑒𝐷 (4.8)

Where A and B are variables based on the diameter ratio.

4.2.9 Reynolds number (Re)

𝑅𝑒𝐷 = 4𝑄𝐸

𝜋𝜂𝐷 (4.9)

29

Where

η = Dynamic Viscosity at 220 °C = 0,0001219 Pa.s

D = inner diameter of pipe = 370,33 mm


The circular reference requires an iterative calculation to determine the flow coefficient, α. To

determine the feedwater flowrate, we assume an initial value for α = 0,7. Continue to substitute α

into the calculation for QE until the difference between successive values for α is smaller than

0,000001. Use the final QE value.

4.2.10 Blowdown Enthalpy at SG1 (hp)

There is however recirculation flow in the SG, due to the wet steam at the top of the SG as per the

Koeberg Safety Analysis Report, mixing with the saturated feedwater. This mixing results in more heat

energy being absorbed in the feedwater and consequently ejected through the blowdown line.

Considering the recirculation flow, the enthalpy of the blowdown can be calculated using the

saturated fluid in feedwater and multiplying it by a recirculation factor. The recirculation factor is

calculated as a function of the relative thermal power. Appendix 16 shows the relationship between

the Recirculation Ratio in the SGs and the level of relative thermal power. The equation for the curve

is given by:

rf = 18.189 – (0.2582 * Qrelt-1) + (0.0011 * Qrel2t-1) (4.10)

where,

rf = the recirculation factor, unitless

Qrelt-1 = the relative thermal power calculated in the previous execution cycle, %

Blowdown Enthalpy

hBD = ((hFW+(rf ×hf) )/(1+rf) (4.11)

where,

hBD = the blowdown enthalpy

hFW = the feedwater enthalpy (kJ/kg)

rf = the recirculation factor (unitless)

hf = the enthalpy of the saturated fluid (kJ/kg)

4.2.11 Blowdown Flow rate at SG1 (Qp)

Blowdown flowrate is measured using a flowmeter:

30

After calculating all variables for Equations 4.1 to 4.9, the thermal power of one steam generator is:


The results of the manual calculations are shown below in Table 4.2. These results are given per

steam generator.

Table 4.2: SHB results

4.3 Independent verification of the manual calculations

As per the license conditions, Koeberg is required to verify the thermal power every day and perform

an independent verification with the SHB once per week. The plant operators in the main control

room, continuously monitor the thermal power by using various indications available to them and

perform an ‘unofficial’ SHB every day (Solomon, 2018). Understandably, it would be very tedious to

manually calculate the SHB every day and therefore various software programmes are used. In this

section we will compare the manual calculations performed in the previous section with the official

SHB programme on KIT. Furthermore we will also perform independent verifications with alternate

computer codes.

4.3.1 Comparison with the Official Secondary Heat Balance (SHB) software used

The same inputs used in Table 4.1 were used in this test to ensure that the results are comparable.

Refer to Appendix 3 for an example of an SHB report that is produced on KIT. The first report is

generated by the Operating Department and provides all the measured inputs and final results, as

computed by KIT. The second report is generated by the testing department who evaluate the inputs

and confirm if the results are acceptable as per the criteria specified in their procedure. They will

determine if any plant parameters should be changed. Because the SHB uses sensors located on the

secondary side of the steam generators, the test is not subject to the large temperature fluctuations

and neutronic disturbances which affect the PHB and RPN systems. These systems will then be

calibrated based on the results from the SHB. The third report is generated by the Engineering

Department and provides an expert analysis of the SHB. The Engineers have information on the

various programming variables and setpoints that could invalidate the test (Adams, 2004). These

setpoints are checked to determine if any drift or software failures has occurred. They utilise an Excel

spreadsheet to perform the analysis.

SHB Manual Calculations (Unit 2 - 10 January 2020)

Parameter SG 1 SG 2 SG 3

Steam Enthalpy (kJ/kg) 2791.31 2792.18 2791.10

Blowdown Enthalpy (kJ/kg) 1108 1108.84 1107.9

Feedwater Enthalpy (kJ/kg) 945.0 946.07 946.48

Feedwater flow (kg/s) 504.83 505.89 495.27

TotalThermal Power (MW) 921.52 922.87 905.86

Primary pump power(MW) 10

TOTAL 2740.25 MW (98.75%)

31

The results of the manual calculations performed in section 4.2 was compared with the results from

the SHB programme. Table 4.3 contains the comparison.

Table 4.3: Comparison of results: Manual calculations versus SHB Programme

The difference between the manual calculations and the SHB programme is 0,17%. This shows a

good correlation between the manual method and automated SHB.

4.4 Compilation of SHB using alternate coding systems

In order to provide more flexibility in the analysis of the SHB and to provide the capability for future

development, the source code was re-written in Microsoft Excel VBA and Python. The new code will

not replace the official SHB test on KIT but will assist with research and fault finding. It will also be

used to identify improvement opportunities. One of the changes includes the use of different steam

tables. Currently, the enthalpies, specific volume and dynamic viscosity are obtained from the ASME

1997 steam property calculations which are programmed in the automated SHB. Whereas Excel and

Python uses later versions of the steamtables and therefore it is expected that the results will differ

slightly (Verein Deutscher Ingenieure -VDI, 2010; Mantey, 2013).

4.4.1 Microsoft Excel VBA Code

The SHB was programmed into Excel using the formula presented earlier in this section. Appendix 17

contains additional detail and screenshots of the VBA code. This was done by following these steps:

Importing of data

The KIT system is a central computer system that interfaces with all plant instruments to

provide data acquisition, processing and display of the data to plant personnel. Some parts of

the system has a Human-Machine Interface (HMI) where the plant can be remotely operated.

The SHB programme extracts data from KIT and then performs the calculations. To create a

new programme, it should be able to extract the data from KIT. In order to achieve this, a

query was written in Excel to perform a call-up function from the data in KIT.

Once the data was imported to Excel, the average of each parameter was calculated. The

average value was then used in a separate worksheet where all the averaged values were

collated. These average values would be used as the SHB inputs.

In order for Excel to use the steam tables it must be imported as an “Add-in”. The Add-in

named “water97-v13” was loaded.

The calculations were programmed in the Excel worksheet.

A VBA code was compiled for the iterative calculation required for the feedwater flow.

The results were compared with the official SHB programme and the manual calculations.

Table 4.4 shows the comparison of the results.


Calculated SHB Prog Calculated SHB Prog Calculated SHB Prog

Steam Enthalpy (kJ/kg) 2791.31 2794.19 2792.18 2794.18 2791.10 2794.1

Blowdown Enthalpy (kJ/kg) 1108 1107.73 1108.84 1107.61 1107.9 1108.2

Feedwater Enthalpy (kJ/kg) 945.0 946.93 946.07 946.07 946.48 946.48

Feedwater flow (kg/s) 504.83 502.44 505.89 503.09 495.27 493.97

Thermal Power (MW) 921.52 919.74 922.87 921.37 905.86 904.31

TOTAL Thermal Power comparison

Calculated: 2740.25 MW (98.75%) SHB Programme: 2735.4 MW (98.58%)

Overall Difference: 0.17%

32

Table 4.4: Comparison of results: Excel VBA vs manual calculations and SHB Programme for SG1

The results show that the Excel VBA code is comparable with the SHB programme showing a

difference of 0.01% for the total thermal power. During the compilation, the following was noted for

improvement:

i) The orifice and pipe diameters must be manually inserted. An improvement would be to

include these parameters in KIT for automatic import into the SHB programme.

ii) The orifice and pipe thermal expansion coefficients must be manually inserted. An

improvement would be to include these parameters in KIT for automatic import into the

SHB programme.

iii) The blowdown recirculation factor must be manually inserted. An improvement would

be to include these parameters in KIT for automatic import into the SHB programme.

4.4.2 Python Code

The SHB was programmed into Python using the formula presented earlier in this section. Appendix

18 contains further detail and screen shots of the Python coding. This was done by following these

steps:

Importing of data

The KIT system is a central computer system that interfaces with all plant instruments to

provide data acquisition, processing and display of the data to plant personnel. Some parts

of the system has a Human-Machine Interface (HMI) where the plant can be remotely

operated. The Python programme extracts data from KIT by using the same Excel file that

was used in the VBA code. See 4.4.1.1 above.

Once the data was imported to Excel, the average of each parameter was calculated. The

average value was then used in the Python coding as the SHB inputs.

In order for Python to use the steam tables it must be imported. The file “CoolProp” was

used and imported.

Various other files were needed for the functions associated with the equations and use of

the Excel spreadsheets. Files “PropsSI”, “math”, “pi”, “xlsxwriter” and “xlrd” were inported.

The Excel spreadsheet with the data was indexed for use

The feedwater flow calculation was programmed using a while loop for the numerous

iterations.

The output was automatically written into an Excel file.

The results were compared with the official SHB programme, the manual calculations and the Excel

VBA coding. Table 4.5 shows the comparison of the results.

SG 1

Parameter Calculated SHB Prog MS Excel VBA





Thermal Power (MW) 921.52 919.74 919.74

TOTAL Thermal Power comparison (for 3 loops)

2740.25 MW (98.75%)

2735.4 MW (98.58%)

2735.4 MW (98.57%)

33

Table 4.5: Comparison of results: Python versus the other methods for SG1

The results show that the Python code is similar to the SHB programme with a difference of 0.06%.

During the compilation, the following was noted for improvement:

i) The Python code extracts data from Excel and therefore the Excel interface with KIT is

still required.

ii) Similar to the Excel VBA programming, the orifice and pipe diameters as well as the

thermal expansion coefficients must be manually inserted. An improvement would be to

include these parameters in KIT for automatic import into the SHB programme. The

blowdown recirculation factor must also be manually inserted.

4.5 SHB accuracy

The total accuracy of the SHB measurement system is dependent upon the combined accuracy of each

instrument. The measurement uncertainty will largely depend on the instrumentation and therefore

it is important to estimate the accuracy of the instrumentation and other factors. Measuring and test

equipment is only beneficial if they provide information that is reliable and precise. Each measured

parameter in the SHB system must produce meaningful results. It is therefore important to review

instrument behaviour for the quality of the desired overall results. This will be evaluated further in

Chapter 5.

4.6 Conclusion

An energy balance was performed across the steam generators by using the SHB methodology. The

SHB calculations were firstly performed manually to ensure that the methodology for determining the

SHB was correct. When compared to the official SHB reports, the difference between the automated

SHB and the manual calculations was found to be 0.17% which showed a good correlation.

In order to provide more flexibility in the analysis of the SHB the source code was written in Microsoft

Excel VBA and Python.. The results show that the Excel VBA code is comparable with the SHB

programme showing a difference of 0.01% for the total thermal power. The Python code is similar to

the SHB programme with a difference of 0.06%. These small differences are beneficial and could be

further developed to replace the now ageing SHB software. Alternatively it could be used for fault-

finding and research. Both the new programming methods had opportunities for improvement such

as manually inserting information from the physical plant structures (i.e orifice and pipe diameters

etc) into the programmes. It is important to review the accuracy of the instrumentation used in the

SHB.

Parameter SG 1

Calculated SHB Prog MS Excel VBA Python

Steam Enthalpy (kJ/kg) 2791.31 2794.19 2794.19 2794.19

Blowdown Enthalpy (kJ/kg) 1108 1107.73 1107.73 1112.89

Feedwater Enthalpy (kJ/kg) 945.0 946.93 946.93 945.43

Feedwater flow (kg/s) 504.83 502.44 502.44 502.49

TotalThermal Power (MW) 921.52 919.74 919.74 920.6

TOTAL Thermal Power comparison

2740.25 MW (98.75%)

2735.4 MW (98.58%)

2735.4 MW (98.57%)

2737.16 MW (98.64%)

34

CHAPTER 5

ANALYSIS OF SHB SENSITIVITY TO INSTRUMENTATION ACCURACY

5.1. Accuracy of the Measurement System

The total accuracy of the SHB measurement system is dependent upon the combined accuracy of the

instruments and other variables used in the system. In this chapter, we will determine the uncertainty

of the SHB system by evaluating each variable that inputs to the test. The magnitude of each

independent variable's uncertainty is estimated by evaluating the following accuracies. These

accuracies contribute to the total uncertainty:

1. Systematic or Bias Uncertainty

2. Random or Precision error

3. Sensitivity analysis

The combination of these effects will provide a holistic view of the combined accuracy and uncertainty

of the SHB measurement system. It is important that the data collected is accurate. Each parameter

in the system has data requirements that must be satisfied if valid system performance is to be

measured. Measuring the parameter must consider the measurement location as this could affect the

measurement due to pressure differences, height, ambient temperature etc. Sampling frequency is

considered for the accuracy of the data logger. A parameter that has a greater measurement

uncertainty should be taken into account with respect to the ability of the instrument to affect thermal

performance. It is therefore important to review instrument behaviour for the quality of the desired

overall results. The measurement uncertainty of a data point is usually stated as a range and a

probability. It is the result of two types of error: random error and systematic error. The total

measurement system (or loop) uncertainty is typically found by calculating the square root of the sum

of the squares of the uncertainties caused by random and systematic error as shown in the following

equation:

𝑇𝑜𝑡𝑎𝑙 𝐸𝑟𝑟𝑜𝑟 = √𝐸𝑟𝑟𝑜𝑟𝑆𝑦𝑠𝑡𝑒𝑚𝑎𝑡𝑖𝑐2 + 𝐸𝑟𝑟𝑜𝑟𝑅𝑎𝑛𝑑𝑜𝑚

2 (5.1)

5.1.1 Systematic or Bias Uncertainty

The systematic or bias uncertainty is a constant error that can be accounted for by calibration. This

error is an indication of accuracy or bias in the instrument and be corrected because it is usually

repeatable. Systematic uncertainty is associated with the following items:

• Linearity of the instrument

• Reference error (Inherent Instrument error)

Drift of the instrument over time

• Error of the calibration equipment

The Secondary Heat Balance uses the instruments listed in Table 5.1.

35

Table 5.1: List of instrumentation used in the SHB

Measured Parameter

Instrument Label

Input Range

Calibration Range

Nominal Value

at 100% Pn

Unit

Feedwater flow: Loop 1 ARE 051 MD 4-20 mA 0 – 200 115 kPa



Steam Pressure: Loop 1 VVP 017 MP 4-20 mA 4040 – 6940 5000 kPa



Feedwater Temp: Loop 1 ARE 005 MT 4-20 mA 0 – 300 220 ºC



Feedwater Pressure: Loop 2 ARE 003 MP 4-20 mA 4000 – 8000 5250 kPa

Blowdown Flow APG 004 MD 4-20 mA 0 – 40 40 T/hr

5.1.1.1. Linearity of the instrument

Zero and span errors are corrected by performing a calibration. Most instruments are provided with a

means of adjusting the zero and span of the instrument, along with instructions for performing this

adjustment. The zero adjustment is used to produce a parallel shift of the input-output curve. The

span adjustment is used to change the slope of the input-output curve. Linearity may be corrected if

the instrument has a linearization adjustment. If the magnitude of the nonlinear error is unacceptable

and it cannot be adjusted, the instrument must be replaced. Madron et al (2015) proposed a simple

method for OLM. This method is based on linearization of the nonlinear model and its success depends

on the magnitude of the deviation from the linear model. A similar method will be considered for the

instrumentation linearity analysis.

For all the instruments listed above, the calibration certificates states the error obtained for each

measurement point. An example of the calibration certificate is shown in Appendix 4. The SHB

programme uses a data logging system to collect and store the data obtained from the instruments.

At Koeberg this data logging system is called “KIT”. It is important that the error of the KIT system is

taken into account determining the thermal power. So to align the instrumentation, KIT and SHB

programme values, a linearity assessment tool is used to ensure that there are no discrepancies

between the measured values and the KIT calculations. The true input and actual output values

obtained from the calibration certificates are used to determine the linearity error. These values are

used in the tool to calculate the actual slope (gain) and actual intercept. Then the gain error (ratio)

and intercept error (difference) are calculated. The coefficient calculation determines the straight line

equation of the true values entered and then calculates the offset (A0) and gain (A1) in order for the

KIT input to be calibrated to the true value.

36

Each instrument of the SHB is analysed for linearity. Below is an example, showing the linearity analysis

for the feedwater temperature sensors. The information is extracted from the calibration certificate.

See Appendix 5 for the analysis of all the instruments.

By plotting the values on a graph the calibration sequence is not perfectly linear(see figure 5.1).

However, when the instrument is installed on the plant and measures a value between any two

calibration values, it will predict a linear path and provide a reading that is not perfectly aligned with

the calibration values. This prediction is shown in red. To correct the linearity, coefficients of linearity

are used to adjust the signal so that the measured values are perfectly aligned with the calibration

values, thereby reducing the uncertainty. These linearity coefficients are programmed into the data

acquisition unit.

Figure 5.1: Linearity graph for SG1 Feedwater temperature sensor

To calibrate the linearity coefficients, the following method is used which is based on the straight line

formula where the slope and intercept (or offset) are calculated. The intent is to solve the equation

for the calibration sequence but use the linear equation parameters to obtain the coefficients.

The straight line (ya) for the calibration sequence:

𝑦𝑎 = 𝑚𝑎 . 𝑥 + 𝑐𝑎 (5.1)

From the table in Appendix 5, the following values are determined for the SG1 feedwater sensor

(1ARE005MT):

Slope (ma)= 18,7 ; intercept (ca)= -74,85

The adjusted line (yb) to the calibrated sequence line

𝑦𝑏 = 𝑦𝑎 . 𝐴1 + 𝐴0 (5.2) where: 𝐴0 = 𝑂𝑓𝑓𝑠𝑒𝑡 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝐴1 = 𝑀𝑢𝑙𝑡𝑖𝑝𝑙𝑖𝑒𝑟 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡

0

50

100

150

200

250

300

5.7 6.7 9.3 12.0 13.6 14.7 16.0 16.8

Tru

e in

pu

t (°

C)

Actual Output (mA)

SG1 Feedwater Temp Sensor Calibration Linear Correction

Calibration sequence

Linear (Calibrationsequence)

37

The solutions are

A0 = 0.0620 ; A1 = 0.9988

And when substituted into equation 5.2, the resulting line will follow the calibration sequence.

From Appendix 5 at 30 °C nominal input

Applying the conversion coefficients to the standard instrumentation formula:

𝑇𝑒𝑚𝑝 = 𝐴0 + 𝐴1 ×𝑅𝑎𝑛𝑔𝑒

𝑚𝐴 × 𝑖𝑛𝑝𝑢𝑡 − 𝑐𝑎𝑙𝑖𝑏𝑟𝑎𝑡𝑖𝑜𝑛 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 (5.3)

𝑇𝑒𝑚𝑝 = 0.0662 + 0.9988 ×300

16 × 5.612 − 75

= 30.252 °C

The true input is 30.263 °C.

Table 5.2 Linearity analysis and Calibration coefficients for SG1 Feedwater

Instrument Nominal Input

°C

True Input during

calibration

Actual output (mA) Adjusted Output with coefficient

% error

Increase Ave

Feedwater Temp Sensor

Input Range:

4-20mA

30 30.26 5.6120 5.6120 30.25208 0.036

50 49.90 6.66180 6.66180 49.91310 -0.020

100 100.09 9.33850 9.33850 100.04324 0.049

150 150.15 12.01690 12.01690 150.20523 -0.034

180 180.08 13.61470 13.61470 180.12937 -0.022

200 199.95 14.67390 14.67390 199.96643 -0.006

225 224.96 16.00770 16.00770 224.94629 0.008

240 239.85 16.80170 16.80170 239.81659 0.015

Ave error 0.024

As can be seen, this produces an output much closer to the actual input. From this output, an average

error can be determined. For this instrument it was determined to be 0.024%. This is done for all the

instruments and the results are included in Appendix 5. Each instrument will have unique design

characteristics and calibration range that needs to be factored into the calculations. For example the

range of the temperature transmitters are 0 to 300 °C while the differential pressure transmitters have

a range of 0 to 200 kPa.

All the coefficients will be input to SHB programme to ensure the entire range is adjusted for the

optimal output. For the purpose of this thesis, the average linearity error will be used to determine

the overall error.

38

5.1.1.2 Reference Error

Reference Accuracy or Error is the baseline accuracy for many instruments and is the percentage of

error associated with the instrument operating within design criteria under reference conditions.

Stated as a percentage of span setting, most manufacturers include the combined effects of linearity,

hysteresis and repeatability. Additionally, all manufacturers specify the reference conditions under

which this performance applies. Because reference accuracy applies only to the stated conditions, it

cannot be considered a measure of overall performance for industrial applications, where conditions

vary. Reference accuracy represents transmitter performance only under “laboratory” conditions. As

an example, Appendix 6 contains the manufacturer supplied data for the feedwater temperature

sensor. Similar data sheets are supplied for all the instruments used in the SHB.

5.1.1.3 Drift

Drift is a source of uncertainty in measurement that should be included in the every uncertainty

budget. It is an influence that you can calculate from your calibration data to see how much the error

in your measurements changes over time. Essentially, drift determines how the error in your

measurement process changes over time, and how much it can contribute to your estimate of

uncertainty in measurement. Drift is determined by reviewing the calibration reports over an

extended period, preferably more than three calibration periods. Hashemian, (2010) reviewed the

impact of ageing and developed various OLM techniques. In the study it was found that vibration,

humidity and temperature contributed to the ageing. It is therefore important that the equipment is

located where these environmental effects are minimised. The location of the SHB instrumentation

has been strategically positioned to reduce these effects. After reviewing the location of the SHB

instruments, the main focus was the feedwater temperature and pressure sensors operate in a high

ambient temperature environment of approximately 50 °C. This is however not a concern because the

specifications of the transmitters allows for operation up to 85 °C.

5.1.1.4 Error in Calibration equipment

A calibration is a comparison of measuring equipment against a standard instrument of higher

accuracy to detect, correlate, adjust, rectify and document the accuracy of the instrument being

compared. The standard instrument will also have a reference error and should be taken into account.

5.1.1.5 Data acquisition error

As mentioned previously, the data processing system, KIT, processes the signals from the instrument to the user interface. The instrument loop of each SHB input was tested for both units. A Fluke 702 instrument calibrator was connected to the instrument loops in place of the instruments and used to inject currents across the measurement ranges. The SHB tests shows result which are within an accuracy of 0.15%. A “watchdog function” is part of the SHB software and is an OLM tool that assists with verifying that

the data used in the SHB is accurate. It provides an interface that determines if the application is

running or not running and the actions to perform when the application is not running. The system

also checks the validity of the SHB outputs. These are invalidated when the input values:

39

Are invalid because it could cause the SHB to be invalid

Falls outside its envelope limits (normal operating modes of the plant)

Exceeds the limit for a transient condition (Each instrument type has its own transient

criterion). The input is considered to be in transient mode when its instantaneous value

(averaged over 10 seconds) differs from its 20 minute average value by more than a

predefined limit.

5.1.2 Combined Systematic Uncertainty The combined systematic uncertainty is a combination of all the items mentioned earlier in sections

5.1.1.1 to 5.1.1.5. As per Mantey, 2013, calculating the Total instrumentation loop (also called the

Systematic error) requires the Root, Sum, Square (RSS) method. This is the square root of the sum of

the squares of all individual uncertainties.

Instrumentation loop error = √ ∑ 𝑈𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 (𝑖)𝑖2

(5.4)

For SHB:

Instrumentation loop or Systematic error = √ Overall Transmitter error2 + 𝐷𝑎𝑡𝑎 𝑎𝑐𝑞𝑢𝑖𝑠𝑖𝑡𝑖𝑜𝑛2

= √𝐸𝑡ℎ𝑒𝑟𝑚𝑜𝑤𝑒𝑙𝑙 2 + 𝐸𝑙𝑖𝑛𝑒𝑎𝑟𝑖𝑡𝑦

2 + 𝐸𝑑𝑟𝑖𝑓𝑡 2 + 𝐸𝑎𝑐𝑐𝑢𝑟𝑎𝑐𝑦

2 + 𝐸𝑐𝑎𝑙𝑖𝑏𝑟𝑎𝑡𝑖𝑜𝑛 2 + 𝐸𝑑𝑎𝑡𝑎 𝑙𝑜𝑔𝑔𝑖𝑛𝑔

2 2 (5.5)

The uncertainty values for the Feedwater Temperature Sensors is shown in Table 5.3. This is based on the manufacturers certificates and calculated values as shown in Section 5.1.1.

Table 5.3: Summary of errors and uncertainties for FW temp sensors

The details of the systematic errors for the other instruments used in the SHB is shown in Appendix 7

5.2 Feedwater flow uncertainty

The feedwater flow is measured by fitting a differential pressure transmitter across an orifice plate.

Differential pressure flow measurement is somewhat unique in that it involves the measurement of

several independent variables, which together with the appropriate equation, calculate the flow rate.

An uncertainty analysis can make it easier to predict the effect of uncertainties in the independent

variables on the uncertainty of the measured flow.

Parameter Error Thermowell 0.5°C = 0.167%

Transmitter Accuracy (Reference Error) (range 0-300°C)

0.2%

Drift 0.2%

Calibration 0.25%

Effect of temperature IGNORE (as per manufacturer)

Linearity 0.024%

Data acquisition error 0.15%

Total error (using formula 5.5) 0.439%

40

Figure 5.4: Schematic of Orifice type water Flowmeter

This method of flow measurement is often used because it eliminates the need for manual

manipulation of data and can be automatically transmitted to an acquisition system. There are many

international standards applicable to this method thereby ensuring that the accuracy of the method

is repeatable.

The differential pressure tansmitters are sourced from Yokogawa who are leaders in the

instrumentation field for these types of transmitters in an industrial application. These transducers

were selected for their sensitivity and stability of performance with a quartz as the pressure -sensing

material which gives excellent stability and reproducibility in pressure measurement.

The ISO standard 5167-1:2003, titled “Measurement of fluid flow by means of pressure differential

devices inserted in circular cross-section conduits running full”, provides the general principles and

requirements applicable to these type of measurement systems. The standard provides the minimum

uncertainty by which the measurement is unavoidable tainted, since the user has no control over

these values. They occur mainly in the calculation of the discharge coefficient and the expansion factor

because of small variations in the geometry of the piping etc.

As per the ISO standard the following equation is used:

𝐹𝑒𝑒𝑑𝑤𝑎𝑡𝑒𝑟 𝐹𝑙𝑜𝑤 𝑈𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 =

√(𝛿𝛼

𝛼)

2

+ (𝛿

)2

+ (2𝛽4

1−𝛽4)2

(𝛿𝐷

𝐷)

2

+ (2

1−𝛽4)2

(𝛿𝑑

𝑑)

2

+1

4(

𝛿∆𝑝

∆𝑝)

2

+1

4(

𝛿𝜌1

𝜌1)

2

(5.6)

Where:

(𝛿𝛼

𝛼) = Discharge coefficient uncertainty

(𝛿

) = Expansion factor uncertainty

(𝛿𝐷

𝐷) = Pipe Diameter ratio uncertainty (0.4% max)

(𝛿𝑑

𝑑) = Orifice diameter ratio uncertainty (0.1% max)

(𝛿∆𝑝

∆𝑝) = Differential Pressure uncertainty

(𝛿𝜌1

𝜌1) = Fluid Density uncertainty

41

It is necessary to know the density and the viscosity of the fluid at the working conditions. In the case

of a compressible fluid, it is also necessary to know the isentropic exponent of the fluid at working

conditions. In this instance, K= 1 because water is considered incompressible.

Differential Pressure uncertainty is given by the manufacturer as the reference uncertainty and is

already calculated as part of the systematic uncertainty. It will therefore be ignored in this calculation.

Fluid Density uncertainty is based on the steam lookup tables and not measured so we can assume

that there is no uncertainty.

Therefore:

𝐹𝑒𝑒𝑑𝑤𝑎𝑡𝑒𝑟 𝐹𝑙𝑜𝑤 𝑈𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦

= √0.65462 + 0.07932 + (2 ∗ 0.69264

1 − 0.69264)

2

∗ (0.4)2 + (2

1 − 0.69264)

2

(0.1)2

= 0.583 %

The detailed calculations for the feedwater inaccuracy is provided in Appendix 8. Janzen et al. (2014)

investigated feedwater flow measurements using ultrasonic flowmeters and found the best

performance to have a relative error of ±8 %. In some cases the error was more than 10%. The

orifice system in the SHB produces an uncertainty of 0.583 %, which is a significant improvement

when compared to non-intrusive systems.

5.3 Random or Precision Error

Random uncertainty is a description of how much variation measurements have and is an indication

of measurement device repeatability and the stability of measurement quality. Vande Visse (1997)

provides the standard for the Instrument loop accuracy. Random error results from unpredictable

variations and will be seen if there are repeated discrepancies in the measured parameter. Random

errors of a measurement result cannot be compensated by correction. They can be minimized or

reduced by increasing the number of samples, increasing the accuracy of the measurement device or

by incorporating a measurement procedure that reduces sources of error.

It is important to have sufficient data to ensure an adequate calculation of random error. However

larger samples could also introduce random errors. For example, an hour of data collected at a

frequency of at least one data point per minute should be adequate to calculate the overall

uncertainty. Collecting data over a full day would introduce random errors due to the increased

possibility of an error occurring. It is therefore important that the data quality is good. Random

uncertainty is calculated by applying the following equation:

𝑅𝑎𝑛𝑑𝑜𝑚 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 =𝑆𝑡×

𝑠

�̅�

√𝑛× 100 (5.7)

Where: St = student t-value (from chart) S = standard deviation �̅� = mean n = count

42

Using the SHB test from 9 Jan 2020, the random uncertainty calculations are tabulated in Appendix 9

showing that the random uncertainty for each instrument is much smaller that the systematic

uncertainty. This is due to the large number of data points that is recorded in a SHB test. Over 3 hours,

the KIT system records 1800 data points. Due to the large “n” count, the uncertainty in equation 5.7

is significantly reduced.

5.4 Influence Factor / Sensitivity

The influence factor or sensitivity is the impact which a measured parameter can have on the result.

Different instruments in the SHB system have different sensitivities because the influence that they

have on the outputs, differ. These sensitivities show the amount of change that occurs in the

calculated result per unit change in the input variable. For example a 1% change in feedwater

temperature has a smaller effect on the SHB result compared to a 1% change in feedwater flow. This

provides valuable information, including:

• A prioritized list of instruments most significantly impacting performance parameters

• Recommendation for any instrument additions

• Recommendation for instrument replacements and improvements

• Recommendation for improvements in calibration techniques

• Recommendation for increased data collection frequency

The sensitivity of all the SHB instruments was checked to determine how much influence the errors

and uncertainties could affect the SHB result. The test of 8 June 2020 was selected for analysis. The

inputs, outputs and final results were recorded. The inputs were then varied by +1%, one input at a

time. For each change, the SHB was recalculated. This analysis shows the change in SHB result when

only a single input is varied by 1%. Table 5.4 shows the results of the sensitivity analysis. Refer to

Appendix 10 for a more detailed breakdown of the results.

Table 5.4: Sensitivity Analysis

Parameter Full Power value

Systematic Uncertainty

(%)

Random Uncertainty

(%)

% change in Reactor Power

SG1 Temp (°C) 220.03 0.439 0.0002 -0.240

SG2 Temp (°C) 220.02 0.439 0.0002 -0.236

SG3 Temp (°C) 220.27 0.439 0.0002 -0.236

Steam Press (kPa) 4864.40 0.406 0.0039 -0.007

Steam Press (kPa) 4851.10 0.406 0.0038 -0.007

Steam Press (kPa) 4865.90 0.406 0.0042 -0.007

FW Press (kPa) 5190.10 0.406 0.0036 -0.004

FW Diff Press (kPa) 117.64 0.489 0.0557 0.160

FW Diff Press (kPa) 112.69 0.489 0.0559 0.163

FW Diff Press (kPa) 114.79 0.489 0.0563 0.163

SG1 Orifice (m) 0.25601 0.583 - 0.92

SG2 Orifice (m) 0.25601 0.583 - 0.90

SG3 Orifice (m) 0.25601 0.583 - 0.88

The feedwater orifice diameter measurement has the highest impact when compared to the other

instruments. When combining the sensitivity of the differential pressure transmitters and the

43

uncertainties of the feedwater flow calculation, it is clear that errors associated with the feedwater

flow measurement will have a significant effect on the SHB result.

When using the EPRI methodology (Mantey, 2013), the next part of the process to determine the

overall uncertainty by combining the measurement error, uncertainties and sensitivity.

The overall uncertainty is determined by calculating the sum of the square root of each contributing

uncertainty.

𝑇𝑜𝑡𝑎𝑙 𝑈𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 = 𝑆𝑦𝑠𝑡𝑒𝑚𝑎𝑡𝑖𝑐 𝑐𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 + 𝑅𝑎𝑛𝑑𝑜𝑚 𝑐𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 (5.8)

where

𝑆𝑦𝑠𝑡𝑒𝑚𝑎𝑡𝑖𝑐 𝑐𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 = [(𝑆𝑦𝑠𝑡𝑒𝑚𝑎𝑡𝑖𝑐 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦

2) × 𝑆𝑒𝑛𝑠𝑖𝑡𝑖𝑣𝑖𝑡𝑦]

2 (5.9)

𝑅𝑎𝑛𝑑𝑜𝑚 𝑐𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 = [(𝑅𝑎𝑛𝑑𝑜𝑚 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦

√𝑠𝑎𝑚𝑝𝑙𝑒 𝑠𝑖𝑧𝑒) × 𝑆𝑒𝑛𝑠𝑖𝑡𝑖𝑣𝑖𝑡𝑦]

2

(5.10

Using the student-t value from the random uncertainty which provides a probability assessment,

the percentage error is determine by:

𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑈𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 = 𝑆𝑡√𝑇𝑜𝑡𝑎𝑙 𝑈𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 (5.11)

Where St = student-t value available from a table in Mantey, 2013 Table 5.5 provides the total

measurement uncertainty.

Table 5.5: Total Uncertainty

Parameter Total

Uncertainty (%)

SG1 Temp 0.002769

SG2 Temp 0.002686

SG3 Temp 0.002686

Steam Press 0.000002



FW Press 0.000001

FW Diff Press 0.001527



Percentage of Total Uncertainty, % (Eq 5.11)

0.232

The total uncertainty, based on full power equates to 6.387 MW.

5.5 Error analysis

Once all the errors and uncertainties have been determined, their impact needs to be evaluated. The

overall test uncertainty includes all the errors and uncertainties and are added to produce a single

value. This means that the overall uncertainty of the SHB is 0.23% (6.387 MW) even when all

instruments are working perfectly and all test conditions (e.g flow orifices) are as expected. According

to a report published by the IAEA (2008), the result must be evaluated against the expected plant’s

safety analysis, so that the assumptions in the design remain valid. Koeberg’s SAR part 3, chapter 4

states the assumptions used in accident studies. In terms of core thermal power, to account for

44

possible instrumentation errors, the initial power level is assumed to be equal to 102%Pn (Koeberg

SAR, Eskom). Therefore the calculated error of 0.23% is within the allowed inaccuracy of 2% over

nominal full power and does not invalidate any safety assumptions in the design basis. It is also similar

to the uncertainty of 0.347% which was determined by Exelon (2009).

5.5.1 Instrument out-of-tolerance condition

Should an instrument be calibrated and found to be out of the manufacturer’s specified tolerance, or

any of the tolerances (systematic accuracy) described in section 5.1, the instrument should be

evaluated for operability. This is done by evaluating how much the error impacted on the test result.

The SHB is calculated with the error inserted into the affected variable (or input). To aid in this analysis,

a tool was developed, using Excel VBA coding to programme the SHB test and automatically update

the out of tolerance values. The results are contained in Appendix 11.

5.5.2 Adjustment of RPN and PHB

The RPN and PHB measurement systems are adjusted based on the results of the SHB (Salie, 2013).

The errors of the SHB instrumentation will therefore be transferred to the RPN and PHB systems. It is

important that the impact of this change is understood, especially if there are any instrumentation

errors. This is because these measurements are related to the design power of the nuclear reactor

and incorrect adjustments could impact on nuclear safety for the plant and environment. If the reactor

power indication to the plant operator is lower than the actual power, then the condition is considered

unsafe due to the potential for the operator to increase power and cause an actual power that is above

100%. In other words, the indicated power (read in the control room) is lower than the actual power.

It is therefore important to distinguish between adjustments that are unsafe and those that are safe.

In the nuclear industry these are referred to as conservative and non-conservative.

Conservative Adjustments

If the instrument error results in an SHB result that is higher than the actual power, then the

adjustments on RPN and PHB will be from a lower value to a higher value. This higher value

means that the actual power will be lower than the indicated power and result in the

automatic reactor trip threshold (based on RPN) to be reached before the actual power is at

the trip setpoint. This will cause the reactor to shutdown before an over-power condition is

experienced.

Non-conservative Adjustments

If the instrument error results in a decreased SHB result, then the adjustments on RPN and

PHB will be from a higher value to a lower value. This lower value means that the actual power

will be higher than the indicated power. It will thus allow the operator to increase power

based on the indication. This causes the actual power to be higher than the indicated power

and possibly exceed the design criteria for an extended period of time.

5.6 Conclusion

The combination of various errors and uncertainty provides a holistic view of the combined accuracy

and uncertainty of the SHB measurement system. These include the systematic uncertainty, random

uncertainty and sensitivity. From all the parameters analysed in this research, it can be concluded that

45

the total inaccuracy of the SHB is 6.387 MW or 0.232% of the full power value. The uncertainty analysis

has many benefits for the power station such as evaluating which instruments most significantly

impact on performance parameters, recommendations for any instrument improvements, as well as

improvements in calibration techniques. Furthermore, the accuracy of data collection in terms of

sampling and data acquisition can also be evaluated. Another benefit is the ability to analyse the

impact on the SHB after an instrument was found to be out of tolerance when it is removed from

service for calibration. In this way, the overall uncertainty can be evaluated while also checking the

impact of one instrument in relation to the SHB result.

The data processing system, KIT, is very accurate (0.15%) and the random uncertainty is reduced due

to the high volume of data. The system also checks the validity of the SHB outputs thereby ensuring

high quality data. The feedwater flow uncertainty was quantified and found to be much better than

non intrusive measurement methods.

The RPN and PHB measurement systems are adjusted based on the results of the SHB and the errors

of the SHB instrumentation will therefore be transferred to the RPN and PHB systems. Once the

instrumentation uncertainty is quantified and understood, then the adjustments can be made in the

conservative direction to ensure nuclear safety is maintained.

46

CHAPTER 6

STEAM GENERATOR THERMAL HYDRAULIC EFFECTS

6.1 Factors affecting performance in the Steam Generator

In PWR plants, there are several types of steam generators which may be used. In a feedring U-tube

type of steam generator, like those at Koeberg, the feedwater enters a downcomer region and flows

up past the tubes. Over most of the tubes, the secondary flow is saturated. Nearly dry saturated steam

exits from the top of the steam generator after passing through a moisture separator section in the

steam dome. The moisture that is separated from the saturated steam recirculates with the

feedwater. The moisture return path is via the downcomer region between the tube wrapper and the

outer steam generator shell. Figure 4.2 shows the design details of a typical feedring steam generator.

The downcomer flow in SGs can provide unique fitness for service and performance indicators related

to overall thermo-hydraulic performance and safety indicators. (Janzen et al.,2014)

Plant thermal performance can be affected by the capability of PWR steam generators to transfer heat from the reactor coolant to the secondary system. This thermal capability can be reduced by several degradation mechanisms, the three most important being the quantity of plugged tubes, accumulation of deposits on the inside and outside tube surfaces and degradation or overloading of the moisture separators. Typically Steam Generators are built to maintain design performance with an allowable amount of tubes plugged (i.e., 10%). Fouling of the moisture separators increases pressure drop and allows more moisture carryover. Erosion or bypasses around the moisture separators and increased velocity due to power uprates or pressure reductions also increase moisture carryover. The number of plugged tubes should be accounted for and trended. The effect of deposit accumulation is determined by calculation. The resistance to heat transfer of a SG tube is the sum of the conductive resistance of the tube wall, the boundary layer resistance of the primary and secondary fluids, and the resistances resulting from the accumulation of any deposit layers on the inside and outside tube surfaces. The effect of increased resistance requires an increase in reactor coolant temperature or a decrease in secondary side temperature, that is, steam pressure to continue transferring the same amount of heat from the reactor. The thermal resistance of SG tubes varies locally throughout the tube bundle, depending on local coolant conditions and local deposit accumulation. It can be shown that a mean thermal resistance can adequately account for local variation and can be used to evaluate and trend the performance of steam generators. Results obtained from the research done by Sadek and Grgic (2017) showed that the steam generator design is able to effectively transfer heat in accident conditions. It is therefore important that thermal energy measurements across the steam generator reflects the actual heat transfer so that the design assumptions are not challenged. This ensures that the steam generator is not over stressed which could affect the performance of the steam generator in the event of an accident. At Koeberg, the fouling is minimal due to strict chemistry specifications and the effective use of the blowdown system. In refuelling shutdowns at Koeberg, the deposit layer is removed through a process called sludge lancing. Sometimes towards the end of an operational cycle, an increase in thermal resistance can be seen. There are however, no abnormal trends which have been reported from the eddy current inspections, sludge lancing activities and endoscopic inspections (Allie, 2018). The SGs will be replaced in 2021 and the clean tubes will improve thermal efficiency.

47

6.2 Recirculation Flow in the Steam Generator

In the previous version of the SHB, the enthalpy of the blowdown fluid was determined by simply

calculating the enthalpy of the saturated fluid present in the steam generator from the feedwater

line. There is however recirculation flow in the SG, due to the wet steam at the top of the SG, mixing

with the saturated feedwater. This mixing results in more heat energy being absorbed in the

feedwater and consequently ejected through the blowdown line. Considering the recirculation flow,

the enthalpy of the blowdown can be calculated using the saturated fluid in feedwater and

multiplying it by a recirculation factor. This recirculation factor (rf) is calculated using the relative

thermal power. See Appendix 2 for equations related to the blowdown.

The recirculation factor is calculated as a function of the relative thermal power. Appendix 16 shows

the relationship between the Recirculation Ratio in the SGs and the level of relative thermal power.

The equation for the curve is given by:

rf = 18.189 – (0.2582 * Qrelt-1) + (0.0011 * Qrel2t-1) (4.10)

rf = 18.189 – (0.2582 * Qrelt-1) + (0.0011 * Qrel2t-1) (6.1)

where,



Blowdown Enthalpy

h𝐵𝐷 = (ℎ𝐹𝑊+(rf ×hf)

1+𝑟𝑓 (6.2)

where,




hf = the enthalpy of the saturated fluid (kJ/kg)

The SHB programme was modified to include this factor

6.3 Oscillations

Thermal hydraulic characteristics of the water and steam flow inside the steam generator causes fluctuations at various intervals. The current test method uses a real time programme to continuously calculate the instantaneous thermal power output of the reactor, but there is evidence that the water and steam flow oscillate in cycles to produce predictable fluctuations. The data used for the SHB is

48

based on the average of all recorded parameters over a three hour period. The SHB test was analysed to determine the effect of the oscillations. Otgonbaatar (2016) determined the uncertainty by using the normal probability distribution for the parameter which is measured. This is however a very complex methodology but some of the statistical principles were applied to this thesis. The data from the test on 16 March for Unit 2 was reviewed and analysed by performing the

following steps:

1. The data from each of the recorded parameters over the 3 hour sampling period

was reviewed:

The average value was determined

The standard deviation was calculated

The maximum value was recorded

The minimum value recorded

2. The data was divided into three sections, with each section representing one hour of

the sampling time. For each of the three sections, the same four parameters were

recorded as in point 1 above.

3. The recorded values from each of the three sections were individually compared to

the calculated values from the data of the 3 hour period.

Refer to Appendix 15 for the results of the analysis. One of the parameters that were analysed is the

SG differential pressure. Figure 6.1 shows the average for the SG differential pressure taken for the

three periods and subtracted from the average of the full 3hr period.

Figure 6.1: Total average minus Average per period for SG Pressures

When investigating the differential pressure measurement of the three steam generators it can be

seen that the difference between the overall average value and the average value for the third hour

shows a negative result, compared to a positive result for the first two hours. This indicates that the

third hour showed a reduction in differential pressure for all SGs. The differential pressure

measurement is used to determine the flow rate. When looking at the other parameters in Appendix

15, it is evident that all the parameters show a significant change in trend for the third period. This

49

indicates that even though the plant was stable and there was no input by the operators, there was a

more significant change in plant parameters in the third hour which impacts on the overall result.

Further work is required in this area to fully understand the contributing factors. Additional testing is

required to determine if this oscillations are systemic or unpredictable. Once these tests have been

performed and the statistical analysis completed, the cause of these oscillations should be

determined.

When studying the trend for the standard deviation of the SG differential pressure, it is expected that

the trends are inverse to the trends for the average values. This is because the standard deviation is

the difference between the average value and the value furthest away from the average value in that

specific data set. This means that if the average is low, then the standard deviation would naturally be

high. In figure 6.2 we can see that the percentage change for the first hour is different to the other

second and third hours.

Figure 6.2: Standard deviation Analysis for SG Differential pressures

The statistical analysis of the data requires further testing and examination to ensure that the quality

of the data that is collected is good and to identify areas for improvement.

6.4 Conclusion

Plant thermal performance can be affected by the capability of PWR steam generators to transfer heat

from the reactor coolant to the secondary system. At Koeberg, there are no abnormal trends which

have shown that the SGs are significantly affected by the degradation mechanisms mentioned earlier.

Their replacement in 2021 will allow the plant life to be extended beyond the original 40 year period

and will improve the plant thermal efficiency. Recirculation flow in the SG, results in more heat energy

being absorbed in the feedwater and consequently ejected through the blowdown line. This flow must

be taken into consideration when calculating thermal performance of the SGs. Thermal hydraulic

characteristics of the water and steam flow inside the steam generator causes fluctuations at various

intervals. It was found that there are differences in the various intervals. One example noted was the

differential pressure measurement. There was a change in the recorded plant parameters for the third

period when compared to the first two periods. This phenomenon should be further investigated to

identify the root cause.

50

CHAPTER 7

PRIMARY HEAT BALANCE

7.1 Measurement of PHB

As mentioned earlier, the reactor thermal power is also measured using the Primary Heat Balance

(PHB) method. The PHB method measures the reactor power by using instrumentation within the

reactor core as part of the reactor coolant system. The instrumentation used to calculate the PHB is

subject to large temperature fluctuations and as a result, is not as stable or accurate as other

measurement systems. The PHB instrumentation is located in the reactor coolant system which is in

the reactor building. While at power, the reactor building is not accessible and therefore the

instruments can not be calibrated. There are however important elements associated with the PHB

which influence the thermal performance calculations. These will be investigated. Also, the PHB and

SHB are performed simultaneously and the result compared, so it is important to understand the

elements which influence the PHB result.

An important element is that the PHB calculations assume either steady-state conditions or conditions

that are steadily changing; i.e., little variation in rate-of-change of system temperature from one

minute to the next. The fluctuations in the various primary parameters would therefore influence the

PHB result and therefore the sampling rate is an important factor to consider.

Thermal hydraulic characteristics of the primary system are influenced by various factors. The

reactivity in the core is affected by core life, control rod position, dilution and boration. The dynamic

effect of the primary loop flow could also impact the PHB result. The parameters use various

instruments and their accuracy must be considered. This includes the primary pump speed error

because it is dependent on grid frequency as well as the water density that is dependent on

temperature.

Figure 7.1: Spatial layout of the Reactor Coolant System (Courtesy of Eskom)

51

The PHB method calculates the specific enthalpy of each hot leg (piping from the reactor) and cold leg

(piping returned to the reactor) using Steam Table functions. The specific enthalpy difference between

the hot leg and the cold leg is calculated by subtracting the specific enthalpy of the cold leg from the

specific enthalpy of the hot leg for a given loop. The density of the cold leg is found from the steam

tables based on the pressure and temperature in the cold leg. The reactor thermal power for a given

loop is calculated by subtracting the specific enthalpies between the hot leg and cold leg and then

multiplying it by the density and volumetric flow. Refer to figures 7.1 and 7.2 for a graphical

representation of the hot and cold legs.

In their research, Mesquita et al (2014) developed various methods to measure the thermal power.

One method was similar to the PHB whereby a constant reactor power is monitored as a function of

the rise in temperature over time and the system heat capacity. These procedures, fuel temperature,

energy balance and calorimetric were implemented in a nuclear research reactor and obtained an

accuracy of 4%.

The SHB uses sensors located on the secondary side and are not subject to the various effects of the

primary system which impact on the reliability of the PHB and RPN systems. The sensitivity of the PHB

is however still important to understand because the PHB is used for continuous monitoring by the

control room staff. It is compared with the SHB on a daily basis and is calibrated every week by

performing an adjustment on the digital circuitry in the data logger. The instruments can not be

calibrated because they are located inside the reactor core. Different instruments in the PHB system

have different sensitivities because of the influence which the measured parameters have on the

result.

Figure 7.2: Loop layout of Reactor Coolant System. (Courtesy of Eskom)

52

The PHB calculations provide the core thermal power transferred to each loop, the reactor thermal

power, and the relative thermal power as a percentage of the rated thermal power. The calculations,

taken from Glath (2012) assume steady-state conditions and therefore the parameters must be

maintained stable during the test.

7.1.1 Reactor Thermal Output

Wloop = C*WF (7.1)

Where:

Wloop = the loop reactor thermal output

C = calibration constant for fine tuning

WF = the power based on volumetric flow, cold leg density, and delta enthalpy per loop,

WCORE = Σ Wloop for loops 1 to 3

7.1.2 Thermal Power to SGs

WSG = Wloop + Wpump (7.2)

where,

WSG = thermal power transferred to SG (MWt)


Wpump = pump heat less NSSS heat losses for loop

Total Thermal Power = 𝐖𝑻 = ∑ 𝑊SG (7.3)

Relative Thermal Power = 𝐖𝑹 =𝑾𝑻

𝑾𝒓𝒂𝒕𝒆𝒅∗ 𝟏𝟎𝟎 (7.4)

where,

WR = the relative thermal power delivered by core to the reactor coolant, %Pn

WT = the reactor thermal power, MWt

WRATED = the rated thermal power, MWt

7.1.3 Loop thermal power

Wloop = ( FVOL* D* dh ) / 3.6E6 (7.5) Where:

Wloop = the loop power based on volumetric flow, cold leg density, and delta enthalpy

53

FVOL = the volumetric flow in the loop m3/h

D = the fluid density in the cold leg, kg/m3

dh = the delta enthalpy in the loop KJ/kg

3.6E6 = the unit conversion factor

7.1.4 Loop Flow Rate

Fvol = Wloop – Ph * SV / dh * C (7.6)

Wloop = Loop Thermal Power

Ph = Pump Heat Losses

SV = Specific Volume

dh = Specific Enthalpy Difference

C = Conversion Factor (unitless)

The detail of the PHB calculations are given in Appendix 12. Table 7.1 shows the results of the

calculations.

Parameter Abr. Loop1 Loop2 Loop3

Hot Leg temperature THL 303.54 304.62 303.03

Cold Leg Temperature TCL 274.31 273.93 273.91

Pressuriser Pressure Ppzr 15389.27 15389.27 15389.27

Cold leg press PCL 15389.69 15389.69 15389.69

Cold leg volumetric flow (Corrected)

Fvol 24372.76 23103.83 23949.86

Cold Leg Specific Volume VCL 0.001291 0.001291 0.001291

Cold leg density DCL 774.06 774.70 774.74

Cold Leg Enthalpy hCL 1203.30 1201.4 1201.28

Hot Leg Enthalpy hHL 1356.40 1362.44 1353.58

Enthalpy difference dh 153.09 161.04 152.29

Loop Thermal Wloop 802.32 800.67 784.97

Reactor Power MW 2397.97 % 86.41

Table 7.1: PHB manual results

7.1.5 PHB: Comparison with Official PHB

These calculations were compared with the official PHB test for 16 March 2020 which calculated a

PHB thermal power of 86.13% (Figure 7.3). The difference between the manual calculations above

(86.41%) and the automated system is 0.28%.

54

Figure 7.3: Snapshot of PHB report

7.1.6 Programming of PHB using Excel VBA

A similar exercise was performed for the PHB, as was done for the SHB regarding the programming of

Excel using VBA code. This was to provide more flexibility with the source code and even though it

will not replace the official PHB test on KIT it will assist with research and fault finding. It will also be

used to identify improvement opportunities. The same steps as explained in section 4.4 were

performed for the PHB. Appendix 19 contains additional detail and screenshots of the VBA code. This

was done by following these steps:

The Importing of data

Importing the data from the KIT system.

Once the data was imported to Excel, the average of each parameter was calculated.

In order for Excel to use the steam tables it must be imported as an “Add-in”. The Add-

in named “water97-v13” was loaded.

The calculations were programmed in the excel worksheet.

For the analysis, the same test used in section 7.1.5, was used as the input data for the Excel

programme. The result of the VBA code was 86.41% which is a 0.28% difference between the

automated PHB result and the VBA code. Refer to Appendix 19.

7.2 PHB Uncertainty

The uncertainty of the PHB should be considered so that if adjustments are required, the effect will

not exceed the allowable tolerances. The PHB is adjusted based on the results of the SHB and the

uncertainties of the SHB and PHB play a role in the accurate measurement of the reactor power. The

uncertainties in the PHB are due to the following factors:

Uncertainty due to the physical measurement device (transducer/transmitter),

Error of the data acquisition unit (KIT) when resistors are used to convert current to voltage

An example of a measurement device used in the PHB is a RTD (Resistance Temperature Detector)

which is used for temperature measurement in the primary system. This is a unique type of

temperature sensor because it consist of a length of fine wire (the resistor) wrapped around a ceramic

or glass core. The RTD wire is a pure material, typically platinum, nickel, or copper. The material has a

resistance/temperature relationship which is used to provide an indication of temperature and is able

to withstand high temperatures. Refer to Appendix 13 for the calculation of the PHB uncertainties

associated with all the instruments used for the PHB.

The uncertainty of the test developed by Mesquita et al (2014) was 4% however at Koeberg, the

uncertainty was found to be 0.903% (Equation A13.4). In comparison with the uncertainty of the SHB

(0.232%), the PHB is less accurate and have more factors that contribute to the total uncertainty.

55

7.3 PHB Sensitivity analysis

The influence factor or sensitivity is the impact which a measured parameter can have on the result.

Different instruments in the PHB system have different sensitivities because of the influence which

the measured parameters have on the result. These sensitivities show the amount of change that

occurs in the calculated result per unit change in the input variable. The same analysis was done for

the PHB as was done for the SHB. The sensitivity of all the PHB instruments were checked to determine

how much influence the errors and uncertainties could affect the result. Detail of the sensitivity

analysis are contained in Appendix 14. A summary of the results per loop are shown below in

Table 7.2.

Table7.2: Sensitivity analysis of loop

Using the same formula used for the SHB analysis (5.8 – 5.11), we find that the sum of the combined

uncertainties equate to 0.305 % and is equivalent to 8.45 MW in total (Table A14-2). When compared

with the uncertainty for the SHB, which is 6.38 MW (from Table 5.4), it can be concluded that the

uncertainty and sensitivity of the PHB is higher in comparison to the SHB.

7.4 Reactor Coolant Pump

The reactor thermal output for a given loop is found by multiplying the specific enthalpy difference

for the hot leg and cold leg by the density and by the loop volumetric flow (calculated as a function of

the ratio between nominal and current reactor coolant pump speed), see Equation 7.5. It can clearly

be seen that a change in reactor coolant pump speed affects the loop flow calculation. A change in

the pump speed during the 3 hour average will therefore alter the PHB. According to Maroka (2015)

the PHB is consistently higher than the SHB and due to various parameters used in the calculation of

the PHB, including the reactor coolant pump speeds, it will affect the relation between the PHB and

SHB.

Based on the sensitivity analysis, shown in Table 7.1, the sensitivity of the pump speed is 0.21%. The

parameter with the highest impact on the PHB result, is the hot leg temperature, with a sensitivity of

0.63%. This is unlike the SHB, where the measurement of the feedwater flow has the greatest impact

on the SHB result as opposed to the feedwater temperature (refer to Section 5.2). With a lower

sensitivity, the changes in speed due to grid transients will not exceed the allowed error and will still

be smaller than the error contributed by the RTDs which measure the hot and cold leg temperatures.

Parameter Sensitivity:

Effect of error (%)

Hot Leg Temperature 0.6307

Cold Leg Temperature -0.5794

Pressurizer Pressure -0.0355

Specific Volume 0.0258

Hot Leg Enthalpy 0.2820

Cold Leg Enthalpy -0.2628

Reactor Coolant Pump Speed 0.2100

56

The pump speed accuracy is shown as 0.14% which equates to 3.09 rpm. See Appendix 13. The pump

speed was analysed and the standard deviation over the three hour period (which consists of 1937

data points) was found to be only 4.24 rpm while operating at a nominal speed of 1490 rpm. This

standard deviation is only slightly higher than the speed accuracy. The deviations in the speed will

therefore not have a major impact on the accuracy of the PHB and therefore will not significantly

affect relationship between the PHB and SHB.

7.5 Conclusion

The instrumentation used to calculate the PHB is subject to large temperature fluctuations and as a

result, is not as accurate as other measurement systems such as the SHB. An important element is

that the PHB calculations assume either steady-state conditions or conditions that are steadily

changing. The PHB was calculated manually for a period at steady state conditions and the results

were compared with the official computed PHB test. The results showed a good correlation with a

difference of 0.28%. The PHB was programmed in Excel for use as a trouble shooting and fault finding

tool. The benefit is that each instrument can be individually altered to show the expected change in

the result. This is useful for when instruments become defective and the impact on the PHB needs to

be determined. It will also assist with estimating the uncertainty due to thermohydraulic effects.

The instrument and KIT errors were used to determine the PHB uncertainty which was calculated as

per EPRI, Mantey (2013). It was found that the sum of the combined uncertainties was found to be

0.903% and is less accurate than the SHB.

The combination of the sensitivity and the uncertainties equate to 0.305 % which is equivalent to 8.45

MW of full power. This is higher than the combined value for the SHB, which is 6.38 MW. This shows

that the PHB is more sensitive and have more uncertainties, in comparison to the SHB.

The primary pump speed sensitivity was evaluated in terms of the accuracy and standard deviation

and found to be smaller than other inputs to the PHB such as the hot leg temperature.

57

CHAPTER 8

SUMMARY AND RECOMMENDATIONS

The Secondary Heat Balance at Koeberg nuclear power station is an energy balance across the steam

generators which are used to transfer the heat from the reactor to the turbine. The SHB uses

instrumentation located on the secondary system of the steam generators as opposed to the

instruments for other power measurement systems which are located inside the reactor core.

Improved accuracies in the SHB will result in a more accurate representation of the thermal power

generated in the core. This thesis analysed the accuracy of the instrumentation, the sensitivity of the

results and the uncertainties in SHB system.

The SHB calculations were firstly performed manually to ensure that the methodology for determining

the SHB was correct. The difference between the official SHB programme and the manual calculations

performed in this thesis was found to be 0.17%

In order to provide more flexibility in the analysis of the SHB and for future development, the source

code for the SHB was written in Excel VBA and Python. The new code will be used in research, fault

finding and to identify improvement opportunities. The manual calculations were used to develop the

Excel VBA code and showed a difference of 0.01% between them. The Python code shows a difference

of 0.06%. These small differences show that the programming software could be beneficial to further

develop and replace the now ageing SHB software.

The SHB is important to nuclear safety and the accuracy must comply to the license conditions as

issued by the National Nuclear Regulator. The combination of various errors and uncertainty provides

a holistic view of the combined accuracy and uncertainty of the SHB measurement system. These

include the systematic uncertainty, random uncertainty and sensitivity. From all the parameters

analysed in this research, it can be concluded that the total inaccuracy of the SHB is 6.387 MW or

0.232% of the full power value. This is in line with the current expectations from the NNR who have

specified a total inaccuracy of 2%.

The data processing system, KIT shows good accuracy and the random uncertainty is reduced due to

the high volume of data. The system also checks the validity of the SHB outputs thereby ensuring high

quality data. The feedwater flow uncertainty was quantified and found to be much better than non

intrusive measurement methods.

Thermal hydraulic characteristics of the water and steam flow inside the steam generator causes

fluctuations at various periods. It was found that there are variations in the data for the different

periods within a test. One example noted was the differential pressure measurement. There was a

change in the recorded plant parameters for the third period when compared to the first two periods

of the test duration. This phenomenon should be further investigated to identify the root cause.

The RPN and PHB measurement systems are adjusted based on the results of the SHB and the errors

of the SHB instrumentation will therefore be transferred to the RPN and PHB systems. To analyse

these errors, the PHB was calculated manually at steady state conditions and the results were

compared with the official computed PHB test. The results showed a good correlation with a

difference of 0.28%. The PHB was programmed in Excel for use as a trouble shooting and fault finding

tool, similar to the method used for the SHB. This is beneficial in that each instrument can be

individually altered to show the expected change in the result. If adjustments are made based on a

defective SHB result, this tool can be used to calculate the PHB with the induced error of the defect.

58

It will also assist with estimating the uncertainty due to thermohydraulic effects. The combination of

the sensitivity and the uncertainties equate to 0.305 % which is equivalent to 8.45 MW of full power.

This is higher than the combined value for the SHB, which is 6.38 MW. This shows that the PHB is more

sensitive and have more uncertainties, in comparison to the SHB.

The accurate measurement of power generated by the reactor core provides confidence that the plant

is operating safely within its design capability. This ensures that the personnel, plant and public are

protected at all times. Nuclear safety is a key objective in the nuclear industry and the SHB helps in

achieving this objective.

59

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Koeberg Safety Analysis report Part 3, Chapter 4 [Controlled Disclosure]

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61

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62

APPENDIX 1

CALCULATIONS OF CONTROLLED VOLUME ANALYSIS

63

At Point 1 (Saturated Liquid)

T1= 30 °C (measured)

P1 = 4.2 kPa (measured)

h1 = hf1 = 124.68 kJ/kg (by interpolation)

V1 = Vf = 0.0001004 m3/kg

At Point 2

T2 = 30.4 °C (measured)

P2 = 4 MPa (measured)

Wpump in = V1(P2-P1) (A1.1)

= (0,001004) (4000 – 4.2)

= 4.01 kJ/kg

h2 = h1 + Wpump

= 124.68 + 4,01

= 128.69 kJ/kg

At Point 3 (Sub-cooled liquid)

T3 = 181 °C (measured)


h3= 767.7 kJ/kg (interpolation)



P4 = 7.4 MPa (measured)

h4= 943.62 kJ/kg (interpolation)

Wpump in = V3(P4-P3) (A1.2)

= (0.001128) (7400-4000)

= 3.84 kJ/kg

64

h4 = h3 + Wpump (A1.3)

= 767.7 + 3.84

= 771.5 kJ/kg




H5= 948.3 kJ/kg (interpolation)

At Point 6 (Saturated liquid)



H5= 948.3 kJ/kg (interpolation)

At Point 7 (Wet steam)



x = 0.9975 (determined during commissioning tests)

h6 = hf + x hfg (A1.4)

= 1154.23 + (0.9975)(1640.1)

= 2790.1 kJ/kg

s6 = sf + x sfg (A1.5)

= 2.92 + (0.9975)(3.0553)

= 5.96 kJ/kg K



s7 = s6 = sf7 + x sfg7 (A1.6)

5.96 = 2.179 + x(4.374)

x = 0.866

65

h7 = hf + x hfg (A1.7)

= 781.34 + (0.866)(2000.4)

= 2513.6 kJ/kg

At Point 9 (Superheated steam)



h8 = 2923 kJ/kg (double interpolation)

s8 = 6.88 kJ/kg.K (double interpolation)


P9 = 4.2 kPa (measured)

s9 = s8 = sf9 + x sfg9 (A1.8)

6.88 = 0.432 + x(8.024)

x = 0.81

h9 = hf + x hfg (A1.9)

= 124.86 + (0.81)(2429)

= 2092.4 kJ/kg

66

APPENDIX 2

SECONDARY HEAT BALANCE CALCULATIONS

Showing all calculations for SG1 from SHB test performed on Unit 2 on 10 January 2020. The same

calculations are repeated for SG2 and SG3 and the results are provided at the end of this Appendix.

Table A2-1: SHB measured inputs

SG1

Parameter Value

Feedwater Pressure 5382 kPa

Feedwater Temp 220.3 °C

Blowdown Flow 3.77 kg/s

Steam Pressure 5004 kPa

Steam Temp 263 °C

Steam quality 0.9975

3.3.1 Steam Enthalpy at SG1 outet (hv)

At 5004 kPa the steam is two phase saturated vapour (by interpolation):

hv = hf + x hfg (A2.1)

= 1155,7 + (0,9975)(1639)

= 2791,31 kJ/kg

s6 = sf + x sfg (A2.2)

= 2,92 + (0,9975)(3,0553)

= 5,96 kJ/kg K

Feedwater Enthalpy at SG1 inlet (hE )

Feedwater enthalpy is sub cooled liquid at 220,3 °C (by interpolation)

hE = hf = 945 kJ/kg

Feedwater Flowrate at SG1 inlet (QE)


4√(2. ∆𝑃. 𝜌 (A2.3)

Where:

α = Flow coefficient

67

ε = Expansion coefficient = 1 for incompressible fluids

d = diameter of orifice

ΔP = Differential pressure across orifice plate

ρ= Density of feedwater

Diameter of orifice (d)

Due to high temperatures the diameter of the orifice will change due to thermal expansion. A fixed

expansion coefficient for stainless steel is used.

d = d0 (1+λd(tE – td0) (A2.4)

= 0,2575 [1+(0,000019)(220,3-23)]

= 258,46 mm

Where:

d0 = measured diameter at room temp = 257,5 mm

λd = expansion coefficient for Stainless steel = 0,000019



Inner diameter of pipe (D)

D = D0 (1+λD(tE – tD0) (A2.5)

= 0,3694 [1+(0,0000128)(220,3-23)]

= 370,33 mm

Where:

D0 = measured diameter at room temp = 369,4 mm

λD = expansion coefficient for Carbon steel = 0,0000128



Diameter ratio ( β)

𝛽 = 𝑑

𝐷 (A2.6)

𝛽 = 0,25846

0,37033

68

= 0,698

Feedwater density (ρ)

At 220,3 °C

𝐷𝑒𝑛𝑠𝑖𝑡𝑦, 𝜌 = 𝑚𝑎𝑠𝑠

𝑉𝑜𝑙𝑢𝑚𝑒=

1

0,001190= 840, 3 𝑘𝑔/𝑚3 (A2.7)

Flow coefficient (α)

𝛼 = 𝐴 + 𝐵. √106

𝑅𝑒𝐷 (A2.8)

Where A and B are variables based on the diameter ratio. The origin of these variables will be

explained later in this thesis.

𝐴 = 0,5922 + 0,4252 [0,3871

(𝐷2𝑥𝛽2+0,254𝐷)+ 𝛽4 + 1,25𝛽16] (A2.9)

= 0,69316

𝐵 = 0,00025 + 0,002325(𝛽 + 1,75𝛽4 + 10𝛽12 + 0,07874𝐷(𝛽16) (A2.10)

= 3,3165 x 10-3

Reynolds number (Re)


𝜋𝜂𝐷 (A2.11)

Where

η = Dynamic Viscosity at 220 °C = 0,0001219 Pa.s

D = inner diameter of pipe = 370,33 mm


The circular reference requires an iterative calculation to determine the flow coefficient, α. To

determine the feedwater flowrate, we assume an initial value for α = 0,7.

69

i. Assign an arbitrary value for alpha: α = 0,7.


4√(2. ∆𝑃. 𝜌 (A2.12)

𝑄𝐸 = (0,7)(1)𝜋0,2582

4√(2)(112𝑥103)(840,3)

= 502,07 kg/s

Where ΔP=112kPa (measured)

ii.


𝜋𝜂𝐷 (A2.13)

𝑅𝑒𝐷 = 4(499,8)

𝜋(0,0001219)(370,33)

ReD = 14085,6

iii. 𝛼 = 𝐴 + 𝐵. √106

𝑅𝑒𝐷 (A2.14)

𝛼 = 1,728 + 3,04𝑥10−3√106

14085,6

= 0,7211

Continue to substitute α into the calculation for QE until the difference between successive values

for α < 0,000001. Use the final QE value.

In this calculation it is 504,83 m3/hr

Blowdown Enthalpy at SG1 (hp)

rf = 18.189 – (0.2582 * Qrelt-1) + (0.0011 * Qrel2t-1) (A2.15)

= 18.189 – (0.2582 * 98.69) + (0.0011 * 98.692)

= 3.42

where,



70

ℎ𝐵𝐷 = ℎ𝐹𝑊+(𝑟𝑓×ℎ𝑓)

1+𝑟𝑓

ℎ𝐵𝐷 = 945 +(3.42×1155.72)

1+3.42

= 1108 kJ/kg

where,




hf = the enthalpy of the saturated fluid (kJ/kg)hp = hf = 1155,72 kJ/kg

Blowdown Flow rate at SG1 (Qp)

Blowdown flowrate is measured using a flowmeter:

Qp = 3,7 kg/s

After calculating all variables for Equation 2 based on results from 3.3.1 to 3.3.11


𝑊𝑆𝐺 = ℎ𝑉 (𝑄𝐸 − 𝑄𝑃) + ℎ𝑃𝑄𝑃 − ℎ𝐸𝑄𝐸 from 4.2

= (2791,3)(502,49 - 3,7) + (1108)(3,7) – (945) (502,49)

= 921,52 MW

The primary pump adds an extra 10 MW to the reactor coolant system and must therefore be

subtracted from the result to obtain the power produced by the reactor. The design full power is

2775MW. The above calculations were performed for loops 2 and 3. Below are the results

Table A2-2: SHB Manual calculations

SHB Manual Calculations (Unit 2 - 10 Jan 2020)






TotalThermal Power (MW) 921.52 922.87 905.86

Primary pump power(MW) 10

TOTAL 2740.25.64 MW (98.75%)

71

APPENDIX 3

EXAMPLE OF SECONDARY HEAT BALANCE REPORTS

Figure A3-1: SHB Report Part A

72

Figure A3-2: SHB Report Part B

73

APPENDIX 4

EXAMPLE OF CALIBRATION CERTIFICATE

74

APPENDIX 5

LINEARITY ANALYSIS

KIT input

M&TE no.

Due date

Cal date

Input range

CAP no.

Nom.

full

power

Nom.

Input True input

Range

check % Error

1ARE051MD 05-Oct-19 0 0.00000 3.99950 3.99830 3.99890 lr int -49.97814251 0.01465 #DIV/0!

27E641632 4-20mA 40 39.95190 7.19270 7.19300 7.19285 lr sl 12.50162702 39.94422 0.019

1RO 164 80 79.91430 10.38840 10.39300 10.39070 lr rsq 0.999999935 79.92255 -0.010

115 120 119.87188 13.58000 13.58800 13.58400 119.84400 0.023

160 159.82887 16.77800 16.78500 16.78150 A0 0.0284 159.81795 0.007

200 199.79310 19.98100 19.98100 19.98100 A1 1.0001302 199.81691 -0.012

1ARE052MD 05-Oct-19 0 0.00000 3.99960 3.99900 3.99930 lr int -50.00020633 -0.00135 #DIV/0!

27E641636 4-20mA 40 39.95190 7.19490 7.19480 7.19485 lr sl 12.5019119 39.94914 0.007

1RO 165 80 79.91430 10.39150 10.39600 10.39375 lr rsq 0.999999926 79.94150 -0.034

115 120 119.87188 13.58000 13.59200 13.58600 119.85073 0.018

160 159.82887 16.77800 16.78600 16.78200 A0 0.0074 159.80685 0.014

200 199.79310 19.98200 19.98200 19.98200 A1 1.000153 199.81297 -0.010

1ARE053MD 05-Oct-19 0 0.00000 3.99740 3.99600 3.99670 lr int -49.95821811 0.00385 #DIV/0!

27E641637 4-20mA 40 39.95190 7.19240 7.19100 7.19170 lr sl 12.50083399 39.94401 0.020

1RO 166 80 79.91430 10.38810 10.39300 10.39055 lr rsq 0.999999961 79.93230 -0.023

115 120 119.87188 13.58100 13.58800 13.58450 119.85934 0.010

160 159.82887 16.77800 16.78300 16.78050 A0 0.0451 159.81201 0.011

200 199.79310 19.98000 19.98000 19.98000 A1 1.0000667 199.80842 -0.008

1VVP017MP 06-Oct-19 4040 4035.25800 3.95310 3.99015 3.97163 lr int 3314.016877 4035.05576 0.005

A300-195 4-20mA 4770 4764.40100 7.97528 8.00583 7.99056 lr sl 181.5475983 4764.68284 -0.006

1RO 172 5000 5500 5493.54400 11.98730 12.02180 12.00455 lr rsq 0.999999958 5493.41397 0.002

6220 6212.69900 15.95760 15.97790 15.96775 6212.92340 -0.004

6940 6931.85400 19.92680 19.92680 19.92680 A0 -6.4261 6931.67940 0.003

A1 1.0016419

1VVP018MP 06-Oct-19 4040 4035.25000 3.95556 3.99238 3.97397 lr int 3312.979169 4034.10015 0.028

A300-197 4-20mA 4770 4764.39200 7.98890 8.02123 8.00507 lr sl 181.4610577 4765.58694 -0.025

1RO 173 5000 5500 5493.53400 12.00320 12.03360 12.01840 lr rsq 0.999999314 5493.85099 -0.006

6220 6212.68700 15.97600 15.98800 15.98200 6213.09007 -0.006

6940 6931.84100 19.93870 19.93870 19.93870 A0 -5.8810 6931.07707 0.011

A1 1.0011645

1VVP019MP 06-Oct-19 4040 4035.24700 3.94051 3.97228 3.95640 lr int 3319.64469 4034.56446 0.017

A300-198 4-20mA 4770 4764.38900 7.98207 8.01558 7.99883 lr sl 180.6997955 4765.03074 -0.013

1RO 174 5000 5500 5493.53000 12.01280 12.05170 12.03225 lr rsq 0.999999771 5493.86982 -0.006

6220 6212.68300 15.99870 16.02320 16.01095 6212.82011 -0.002

6940 6931.83600 19.98760 19.98760 19.98760 A0 14.7077 6931.39996 0.006

A1 0.9969644

1ARE005MT 16-May-20 30 30.26300 5.61200 5.61200 lr int -74.85140829 30.25208 0.036

9815109 4-20mA 50 49.90300 6.66180 6.66180 lr sl 18.72834061 49.91310 -0.020

1Y 161 100 100.09200 9.33850 9.33850 lr rsq 0.999999804 100.04324 0.049

150 150.15400 12.01690 12.01690 150.20523 -0.034

180 180.08900 13.61470 13.61470 A0 0.0620 180.12937 -0.022

200 199.95400 14.67390 14.67390 A1 0.9988448 199.96643 -0.006

220 225 224.96500 16.00770 16.00770 224.94629 0.008

240 239.85200 16.80170 16.80170 239.81659 0.015

1ARE006MT 14-May-20 30 31.31500 5.69400 5.69400 lr int -75.3730417 31.51078 -0.625

9815108 4-20mA 50 49.90600 6.66620 6.66620 lr sl 18.77129852 49.76024 0.292

1Y 162 100 99.68700 9.31700 9.31700 lr rsq 0.999996713 99.51919 0.168

150 149.90900 12.00070 12.00070 149.89572 0.009

180 179.70700 13.60100 13.60100 A0 -0.2878 179.93543 -0.127

200 199.65100 14.64950 14.64950 A1 1.0011359 199.61714 0.017

220 225 225.09300 16.00440 16.00440 225.05037 0.019

240 240.04100 16.80190 16.80190 240.02048 0.009

1ARE007MT 14-May-20 30 31.23000 5.69100 5.69100 lr int -75.05558431 31.55874 -1.053

79914 4-20mA 50 49.99100 6.66590 6.66590 lr sl 18.73384781 49.82237 0.337

1Y 163 100 99.71600 9.32210 9.32210 lr rsq 0.999994378 99.58322 0.133

150 149.91800 12.00350 12.00350 149.81616 0.068

180 179.69300 13.58630 13.58630 A0 -0.1202 179.46809 0.125

200 199.65300 14.66860 14.66860 A1 0.9991386 199.74374 -0.045

220 225 225.08900 16.02640 16.02640 225.18056 -0.041

240 240.05800 16.82680 16.82680 240.17513 -0.049

1ARE003MP 06-Oct-19 4000 3995.36300 3.97724 3.99821 3.98773 lr int 2999.291598 3995.16899 0.005

A300-578 4-20mA 5000 4994.20400 7.97971 8.00068 7.99020 lr sl 249.7357623 4994.72884 -0.011

1RO 93 5250 6000 5993.04500 11.97980 11.99710 11.98845 lr rsq 0.999999782 5993.23605 -0.003

7000 6991.88600 15.97690 15.98820 15.98255 6990.70561 0.017

8000 7990.72700 19.98950 19.98950 19.98950 A0 2.4625 7991.38427 -0.008

A1 0.998943

1APG004MD 0 0.00000 4.01400 4.01700 4.01550 lr int

15750 0-500mV 15 10.00000 8.00200 8.02200 8.01200 lr sl

6 30 20.00000 11.99600 12.03900 12.01750 lr rsq

40 40 45 30.00000 16.00400 15.99700 16.00050

60 40.00000 19.97800 19.97800 19.97800 A0 0.0000

A1 1

Actual output

Incr. Decr. Avg.

Conversion

coefficients

75

The straight line (ya) for the calibration sequence:

𝑦𝑎 = 𝑚𝑎 . 𝑥 + 𝑐𝑎 (A5.1)

From the table in Appendix 5, the following values are determined for the SG1 feedwater sensor

(1ARE005MT):

Slope (ma)= 18,7 ; intercept (ca)= -74,85

The adjusted line (yb) to the calibrated sequence line

𝑦𝑏 = 𝑦𝑎 . 𝐴1 + 𝐴0 (A5.2) where: 𝐴0 = 𝑂𝑓𝑓𝑠𝑒𝑡 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝐴1 = 𝑀𝑢𝑙𝑡𝑖𝑝𝑙𝑖𝑒𝑟 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 This equates to

𝐴0 = 𝑐𝑏 −𝑚𝑏

30016

(0 −300

16× 4)

and

𝐴1 =16

300× 𝑚𝑏

76

APPENDIX 6

MANUFACTURER SUPPLIED DATA FOR FEEDWATER TEMPERATURE SENSOR

77

APPENDIX 7

SYSTEMATIC ERRORS FOR ALL INSTRUMENTS USED IN THE SHB

Instrumentation loop error = √ ∑ 𝑈𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 (𝑖)𝑖2

For SHB:

Instrumentation loop or Systematic error = √ Overall Transmitter error2 + 𝐷𝑎𝑡𝑎 𝑎𝑐𝑞𝑢𝑖𝑠𝑖𝑡𝑖𝑜𝑛2

= √𝐸𝑡ℎ𝑒𝑟𝑚𝑜𝑤𝑒𝑙𝑙 2 + 𝐸𝑙𝑖𝑛𝑒𝑎𝑟𝑖𝑡𝑦

2 + 𝐸𝑑𝑟𝑖𝑓𝑡 2 + 𝐸𝑎𝑐𝑐𝑢𝑟𝑎𝑐𝑦

2 + 𝐸𝑐𝑎𝑙𝑖𝑏𝑟𝑎𝑡𝑖𝑜𝑛 2 + 𝐸𝑑𝑎𝑡𝑎 𝑙𝑜𝑔𝑔𝑖𝑛𝑔

2 2

(A7.1)

For feedwater sensors

= √0.1672 + 0.0242 + 0.22 + 0.252 + 0.22 + 0.152

= 0.439 %

Table A7-1: Systematic errors for SHB

Parameter FW

Temp FW Pres FW DP

SG Steam Press

Feedwater flow

Thermowell 0.5°C

(0.167%) N/A N/A N/A N/A

Linearity 0.024 % 0.009 % 0.014 % 0.004 % N/A

Transmitter Accuracy

0.2 % 0.2 % 0.040 % 0.2 % N/A

Drift 0.2 % 0.2 % 0.1 % 0.2 % N/A

Calibration accuracy

0.25 % 0.25 % 0.145 % 0.25% N/A

Static Pressure effect

N/A N/A 0.145 % N/A N/A

Effect of temperature

IGNORE IGNORE 0.425 % IGNORE N/A

Data acquisition error

0.15 % 0.15 % 0.15 % 0.15 % N/A

Orifice Plate N/A N/A N/A N/A 0.583 %

TOTAL ERROR 0.439 % 0.406 % 0.489 % 0.406 % 0.583 %

78

APPENDIX 8

FEEDWATER FLOW UNCERTAINTIES


= √(𝛿𝛼

𝛼)

2

+ (𝛿휀

휀)

2

+ (2𝛽4

1 − 𝛽4)

2

(𝛿𝐷

𝐷)

2

+ (2

1 − 𝛽4)

2

(𝛿𝑑

𝑑)

2

+1

4(

𝛿∆𝑝

∆𝑝)

2

+1

4(

𝛿𝜌1

𝜌1)

2

Where:

Discharge coefficient uncertainty (𝛿𝛼

𝛼) :

For 0.6 < β < 0.75

Then 𝛿𝛼

𝛼 = (1.667β - 0.5) %

= (1.667*0.692 – 0.5)

= 0.6546 %

Expansion factor uncertainty (𝛿

) = 3.5*𝑑𝑃

𝑝1∗𝐾 %

= 3.5*117.67

5190∗1

= 0.0793 %

Where κ = isentropic exponent = 𝐶𝑝

𝐶𝑣 across the orifice. It is necessary to know the density and the

viscosity of the fluid at the working conditions. In the case of a compressible fluid, it is also necessary

to know the isentropic exponent of the fluid at working conditions. In this instance, K= 1 because

water is considered incompressible and therefore:

𝑃𝑖𝑝𝑒 𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟 𝑟𝑎𝑡𝑖𝑜 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦: (𝛿𝐷

𝐷) = 0.4% max

𝑂𝑟𝑖𝑓𝑖𝑐𝑒 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟 𝑟𝑎𝑡𝑖𝑜 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑛𝑡𝑦 ∶ (𝛿𝑑

𝑑) = 0.1% max

𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑙 𝑃𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 ∶ (𝛿∆𝑝

∆𝑝) is given by the manufacturer as the reference

uncertainty and is already calculated as part of the systematic uncertainty. It will therefore be

ignored in this calculation.

𝐹𝑙𝑢𝑖𝑑 𝐷𝑒𝑛𝑠𝑖𝑡𝑦 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 (𝛿𝜌1

𝜌1) is based on the steam lookup tables and not measured so we

can assume that there is no uncertainty.

79

Therefore:


= √0.65462 + 0.07932 + (2 ∗ 0.69264

1 − 0.69264)

2

∗ (0.4)2 + (2

1 − 0.69264)

2

(0.1)2

= 0.583 %

80

APPENDIX 9

RANDOM UNCERTAINTIES

Applying to the SG1 FW Temp

𝑅𝑎𝑛𝑑𝑜𝑚 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 =𝑆𝑡 ×

𝑠�̅�

√𝑛× 100

Where: St = student t-value (from chart) α = confidence level S = standard deviation �̅� = mean n = count

𝑅𝑎𝑛𝑑𝑜𝑚 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦(𝑆𝐺𝐹𝑊𝑇𝑒𝑚𝑝1) =2.045 ×

0.009220.5

√1800× 100

= 0.0002%

Applying the above calculations to all the instruments

Table A9-1: Random Uncertainties

SG1 DP

SG2 DP

SG3 DP

SG1 FW

TEMP

SG2 FW

TEMP

SG3 FW

TEMP

SG1 PRESS

SG2 PRESS

SG3 PRESS

SG2 FW

PRESS

St (n-1, α/2) 2.045 2.045 2.045 2.045 2.045 2.045 2.045 2.045 2.045 2.045

avg 81.77 81.89 78.33 213.1 212.9 213.0 4605.6 4604.7 4616.2 4919.0

stdev 0.945 0.950 0.915 0.009 0.006 0.008 3.735 3.631 3.978 3.657

max 84.48 84.76 81.30 213.09 212.95 213.04 4615.08 4614.39 4625.72 4928.16

min 79.18 78.94 75.46 213.05 212.90 213.00 4591.64 4590.28 4600.24 4905.60

max - min 5.30 5.82 5.85 0.05 0.05 0.05 23.44 24.10 25.48 22.56

Count 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800

Random uncertainty

0.0557 0.0559 0.0563 0.0002 0.0001 0.0002 0.0039 0.0038 0.0042 0.0036

Table A9-1: Random Uncertainties

81

APPENDIX 10

SENSITIVITY ANALYSIS FOR THE SHB

Table A10-1: Sensitivity Analysis of SHB instruments

Initial values of test New values % change in Loop Power

% change in Reactor

Power Parameter Input

value Loop

power Reactor power

Input value +1%

Loop power

Reactor power

SG1 Temp (°C) 220.03 928.4 2753.1 222.23 921.77 2746.5 -0.71 -0.24

SG2 Temp (°C) 220.02 908.6 2753.1 222.22 902.11 2746.6 -0.71 -0.24

SG3 Temp (°C) 220.27 916.1 2753.1 222.47 909.56 2746.6 -0.71 -0.24

SG1 Press (kPa) 4864.40 928.40 2753.10 4913.04 928.21 2752.90 -0.02 -0.01

SG2 Press (kPa) 4851.10 908.60 2753.10 4899.61 908.41 2752.90 -0.02 -0.01

SG3 Press (kPa) 4865.90 916.10 2753.10 4914.56 915.92 2752.90 -0.02 -0.01

FW Press (kPa) 5190.10 908.60 2753.10 5241.90 908.42 2753.00 -0.02 0.00

SG1 Flow (kPa) 117.64 928.40 2753.10 118.80 933.00 2757.50 0.50 0.16

SG2 Flow (kPa) 112.69 908.60 2753.10 113.82 913.16 2757.60 0.50 0.16

SG3 Flow (kPa) 114.79 916.10 2753.10 115.94 920.50 2757.60 0.48 0.16

SG1 Orifice (m) 0.25601 928.40 2753.10 0.25866 954.05 2778.50 2.76 0.92

SG2 Orifice (m) 0.25601 908.60 2753.10 0.25866 933.57 2778.00 2.75 0.90

SG3 Orifice (m) 0.25601 916.10 2753.10 0.25856 940.20 2777.30 2.63 0.88

𝑇𝑜𝑡𝑎𝑙 𝑈𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 = 𝑆𝑦𝑠𝑡𝑒𝑚𝑎𝑡𝑖𝑐 𝑐𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 + 𝑅𝑎𝑛𝑑𝑜𝑚 𝑐𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 (A10.1)

where

𝑆𝑦𝑠𝑡𝑒𝑚𝑎𝑡𝑖𝑐 𝑐𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 = [(𝑆𝑦𝑠𝑡𝑒𝑚𝑎𝑡𝑖𝑐 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦

2) × 𝑆𝑒𝑛𝑠𝑖𝑡𝑖𝑣𝑖𝑡𝑦]

2 (A10.2)

𝑅𝑎𝑛𝑑𝑜𝑚 𝑐𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 = [(𝑅𝑎𝑛𝑑𝑜𝑚 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦

√𝑠𝑎𝑚𝑝𝑙𝑒 𝑠𝑖𝑧𝑒) × 𝑆𝑒𝑛𝑠𝑖𝑡𝑖𝑣𝑖𝑡𝑦]

2

(A10.3)

Using the student-t value from the random uncertainty which provides a probability assessment,

the percentage error is determine by:

𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑈𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 = 𝑆𝑡√𝑇𝑜𝑡𝑎𝑙 𝑈𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 (A10.4)

Where St = student-t value available from a table in Mantey, 2013

82

Table A10-2: Combining error and Sensitivity SHB instruments

Combining error and Sensitivity Parameter FP

value

Systematic

Uncertainty

Random

Uncertainty

Sensitivity Combined Total

Uncertainty Systematic

Contribution

Random Contribution

SG1 Temp 220.03 0.439 0.0002 -0.240 0.002769 1.654E-12 0.002769

SG2 Temp 220.02 0.439 0.0002 -0.236 0.002686 1.604E-12 0.002686

SG3 Temp 220.27 0.439 0.0002 -0.236 0.002686 1.604E-12 0.002686

Steam Press 4864.40 0.406 0.0039 -0.007 0.000002 5.376E-13 0.000002

Steam Press 4851.10 0.406 0.0038 -0.007 0.000002 5.082E-13 0.000002

Steam Press 4865.90 0.406 0.0042 -0.007 0.000002 6.070E-13 0.000002

FW Press 5190.10 0.406 0.0036 -0.004 0.000001 1.129E-13 0.000001

FW Diff Press 117.64 0.489 0.0557 0.160 0.001527 5.289E-08 0.001527

FW Diff Press 112.69 0.489 0.0559 0.163 0.001597 5.566E-08 0.001597

FW Diff Press 114.79 0.489 0.0563 0.163 0.001597 5.649E-08 0.001597

Sum of Total Uncertainty, % (Eq 5.8) 0.013

Percentage of Total Uncertainty % (Eq 5.11) 0.232

Average corrected output, MW 2753.100

Test uncertainty, MW 6.387

83

APPENDIX 11

EXCEL PROGRAMME WITH AUTOMATIC ERROR

Test No : start end

Date : 16-Mar-2020 23:55:00 02:55:00

Parameter SG1 SG2 SG3 SG1 SG2 SG3

offset dp -0.032 -0.100 -0.015 kPa

uncorrected dP 81.772 81.888 78.332

Feed Water dP (z corrected) 81.74 81.79 78.32 kPa 81.74 81.79 78.32

Feed Water Temp 213.08 212.93 213.03 °C 213.08 212.93 213.03

Feed Water Pressure 5020.29 kPa(abs) 5020.29

Steam Pressure 4706.9 4706.1 4717.5 kPa(abs) 4706.9 4706.1 4717.5

Impulse line water head 0.0 kPa (ρgh) 0.0

Steam Pressure (corrected) 4706.9 4706.1 4717.5 kPa(abs) 4706.9 4706.1 4717.5

Steam Quality 0.9975 0.9975 0.9975 0.9975 0.9975 0.9975

Total Blowdown Flow 39.53 t/hr 39.53

Blowdown Flow per Loop 3.66 3.66 3.66 kg/s 3.66 3.66 3.66

Intermediate Results

Feed Water Volumic Mass 851.43 851.62 851.49 kg/m3 851.43 851.62 851.49

Feed Water Enthalpy 912.77 912.10 912.54 kJ/kg 912.77 912.10 912.54

Steam Saturated Enthalpy 2796.53 2796.54 2796.46 kJ/kg 2796.53 2796.54 2796.45

Water Saturated Enthalpy 1135.79 1135.74 1136.48 kJ/kg 1135.80 1135.74 1136.48

Steam Wet Enthalpy 2792.38 2792.39 2792.31 kJ/kg 2792.38 2792.39 2792.31

Blowdown Enthalpy 1095.97 1135.74 1136.48 kJ/kg 1135.80 1135.74 1136.48

Feed Water Dynamic Viscosity 0.00012643 0.00012652 0.00012646 kg/s.m 0.00012643 0.00012652 0.00012646

Orifice Diameter 0.25750 0.25750 0.25751 m 0.25750 0.25750 0.25751

Pipe Diameter 0.36940 0.36950 0.36940 m 0.36940 0.36950 0.36940

Beta 0.69707634

Results 430.24 430.34 421.20 FW flow

Feed Water Flow 430.24 430.34 421.20 430.24 430.34 421.20

Feed Water Flow 1548.9 1549.2 1516.3 t/hr 1548.9 1549.2 1516.3

Flow Coefficient (alpha) 0.6956 0.6955 0.6956 0.6955 0.6955 0.6955

SG Thermal Power (incl PP) 802.47 803.09 785.69 MWth 802.62 803.09 785.69

Reactor Thermal Power (excl PP) 799.14 799.76 782.36 MWth 799.28 799.76 782.36

86.39% 86.46% 84.58% 86.41% 86.46% 84.58%

0.58% 0.65% -1.23% 0.60% 0.65% -1.23%

Power Transfer with RCP 10 MWth 10

Total Reactor Thermal Power 2381.3 MWth 2381.4

% Full Power 85.81 % Pn 85.82

U2 SHB error analysisU2 Secondary Heat Balance

The RPN channels and PHB are calibrated based on the SHB result

Increase results in positive

Increase results in negative

Increase results in positive

increase results in positive

FW1 temp

+ error

FW2 temp+error

Fwpress+error

DP1+ error

DP2 + error

DP3 +error

FW1 +uncertainty

FW2 +uncertainty

FW3 +uncertainty

FW3 temp-error

RESET ALL

FW1 temp- error

FW2 temp- error

Fwpress- error

DP1- error

DP2 - error

DP3 - error

FW3 temp- error

FW1 - uncertainty

FW2 - uncertainty

FW3 - uncertainty

84

APPENDIX 12

PRIMARY HEAT BALANCE

Reactor Thermal Output

Wloop = C*WF MWt

Where:


C = calibration constant for fine tuning

WF = the power based on volumetric flow, cold leg density, and delta enthalpy per loop,

WCORE = Σ Wloop for loops 1 to 3 (A12.1)

Thermal Power to SGs

WSG = Wloop + Wpump (A12.2)

where,

WSG = thermal power transferred to SG (MWt)


Wpump = pump heat less NSSS heat losses for loop

Total Thermal Power = 𝐖𝑻 = ∑ 𝑊SG (A12.3)

Relative Thermal Power = 𝐖𝑹 =𝑾𝑻

𝑾𝒓𝒂𝒕𝒆𝒅∗ 𝟏𝟎𝟎 (A12.4)

where,

WR = the relative thermal power delivered by core to the reactor coolant, %Pn

WT = the reactor thermal power, MWt

WRATED = the rated thermal power, MWt

Loop thermal power

Wloop = ( FVOL* D* dh ) / 3.6E6 (A12.5) Where: Wloop = the loop power based on volumetric flow, cold leg density, and delta enthalpy FVOL = the volumetric flow in the loop m3/h D = the fluid density in the cold leg, kg/m3 dh = the delta enthalpy in the loop KJ/kg

85

3.6E6 = the unit conversion factor

Loop Flow Rate

Fvol = Wloop – Ph * SV / dh * C (A12.5)

Wloop = Loop Thermal Power

Ph = Pump Heat Losses

SV = Specific Volume

dh = Specific Enthalpy Difference

C = Conversion Factor (unitless)

Loop Specific Enthalpy Difference

dh = h [Hot leg] – h [Cold leg] (A12.6)

where,

dh = the delta enthalpy in the loop, kJ/kg

h = the specific enthalpy from the Steam Table, as a function of temperature and pressure, kJ/kg

Th = the temperature in the ith hot leg, °C

P = the pressurizer pressure, Bar(g)

TC = the temperature in the ith cold leg, °C

PC = the cold leg pressure, Bar(g)

Patm = the atmospheric pressure constant, Bar(g)

Cold Leg Volumetric Flow

QVOLcold = (A * B )( QREL)]/100 (A12.7)

where,

QVOLcold = volumetric flow in cold leg, m3/h

A = nominal full power RCP loop flow, m3/h

B = loop Nominal Flow Multiplier, unitless

QREL = the relative flow in the cold leg, percent of nominal

86

Cold leg density:

DCL = 1 / SV[ Cold Leg ] (A12.8)

where,

DCL = fluid density in cold leg, kg/m3

SV = a Steam Table function which provides specific volume as a function of temperature

and pressure

Cold Leg Pressure:

PCL = Ppzr + E

where,

PC = the calculated cold leg pressure, Bar(g)

Ppzr = the pressurizer pressure, Bar(g)

E = an amendable constant to correct for pressure drop across the reactor vessel = 4.2 Bar

The test of 16 March was used for analysis. Below are the results of the calculations are shown

below

Table A12-1: Summary of PHB results

Parameter Abr. Loop1 Loop2 Loop3

Hot Leg temperature THL 303.54 304.62 303.03

Cold Leg Temperature TCL 274.31 273.93 273.91

Pressuriser Pressure Ppzr 15389.27 15389.27 15389.27

Cold leg press PCL 15389.69 15389.69 15389.69

Cold leg volumetric flow (Corrected)

Fvol 24372.76 23103.83 23949.86

Cold Leg Specific Volume VCL 0.001291 0.001291 0.001291

Cold leg density DCL 774.06 774.70 774.74

Cold Leg Enthalpy hCL 1203.30 1201.4 1201.28

Hot Leg Enthalpy hHL 1356.40 1362.44 1353.58

Enthalpy difference dh 153.09 161.04 152.29

Loop Thermal Wloop 802.32 800.67 784.97

Reactor Power MW 2397.97 % 86.41

87

APPENDIX 13

PRIMARY HEAT BALANCE UNCERTAINTIES

RTD accuracy (from manufacturer)

Reference accuracy: 0.1 °C

Influence of operating pressure (used at 15 Mpa but calibrated at atmospheric pressure): 0.07 °C

Repeatability: 0.11 °C

Utilising the root square method to determine the Total RTD Uncertainty:

ΔTRTD = √0.12 + 0.072 + 0.112 = 0.1644 °C

Data acquisition:

Data acquisition accuracy = 0.1%

Hot Leg and Cold Leg Span = 70 °C

Uncertainty due to data acquisition at hot/cold leg = 70*0.1% = +/- 0.07 °C

Combined Uncertainty = √0.072 + 0.072 = 0.09899 °C (for both the hot and cold leg)

Combined data acquisition and RTD error = √0.16442 + 0.098992 = 0.191831°C

Specific Volume Error:

Total Uncertainty = +/- 0.015%

(IAPWS Thermodynamic Properties of Water and Steam, 2007)

Pressurizer Pressure Error

Reference error : 2.03% of Span for range 11.1 to 18.1 MPa (as per manufacturer)

Total Uncertainty = 0.0681 MPa / 15.41 MPa = +/- 0.4419%

Enthalpy Error

For Hot Leg: Temperature = 321 °C, Pressure = 15.41 MPa

Uncertainty = 0.5 kJ /kg (IAPWS Thermodynamic Properties of Water and Steam, 2007)

At full power: Uncertainty = 0.5 / 1423.8 *100= 0.0351%

For Cold Leg: Temperature = 286.6 °C, Pressure = 15.41 bar

88

At full power: Uncertainty = 0.5 / 1273 *100= 0.03927%

Total Enthalpy uncertainty =√Hot leg2 + Cold leg2 = √0.03512 + 0.039272 = 0.05267%

Primary Pump Speed:

0.14% (Manufacturer)

Uncertainty = 0.0014 * 1800 = +/- 2.52 RPM

Total Uncertainty = √1.822 + 2.522 = 3.09684 RPM

Final PHB error

𝐹𝑖𝑛𝑎𝑙 𝑒𝑟𝑟𝑜𝑟 =

√(Total Enthalpy error)2 + (Cold leg error)2 + (Hot leg error)2 +

(Specific Volume)2 + (Pressuriser Pressure error)2 + (Primary pump speed)2 (A13.1)

= 1.56493%

Full power per loop = 925 MW Per Loop

Loop Error = 925 * 1.56493% (A13.2)

= 925 * 0.0156493

= 14.4756 MW

Each loop percent error = Loop error / full power * 100% (A13.3)

= (14.4756 / 2775 )*100

= 0.5216 %

Total error = √∑ 𝐿𝑜𝑜𝑝 𝑒𝑟𝑟𝑜𝑟2 *100% (A13.4)

= √ ∑ 0.00521643230 * 100%

= √ ∑ 0.0052164323

1

= 0.903513 %

89

APPENDIX 14

PRIMARY HEAT BALANCE SENSITIVITY ANALYSIS

Table A14-1: PHB instruments Systematic Errors

Parameter Full Power

value

Error (%) Value after error Loop Power Loop

Power

Sensitivity:

Hot Leg Temperature 312.4 0.1918 (°C) 312.208 928.6 934.45 0.6307

Cold Leg

Temperature

279.2 0.1918 (°C) 279.008 928.6 923.22 0.5794

Pressurizer Pressure 15.41 0.4419 15.477 928.6 928.27 0.0355

Specific Volume 765.8 0.0150 765.950 928.6 928.84 0.0258

Hot Leg Enthalpy 1406.94 0.0351 1407.443 928.6 931.21 0.2820

Cold Leg Enthalpy 1227.832 0.0392 1228.320 928.6 926.16 0.2628

Reactor Coolant

Pump Speed

1485 0.210 1481.881 928.6 930.55 0.2100

Table A14-2: PHB instruments combining Systematic Errors and Uncertainty

Parameter Full Power

value Systematic

Uncert Random uncert

Sensitivity Systematic

Contribution Random

Contribution Combined

contribution

Hot Leg Temperature

321 0.1918 0.0017 0.630734 0.003659 7.955E-10 0.003659

Cold Leg Temperature

286.6 0.191831 0.0009 0.579367 0.003088 1.935E-10 0.003088

Pressurizer Pressure 15.41 0.44 0.0008 0.035537 0.000061 5.182E-13 0.000061

Specific Volume 752.3709 0.015 0.0000 0.025845 0.000000 0.000E+00 0.000000

Hot Leg Enthalpy 1459.2 0.052 0.0000 0.282037 0.000054 0.000E+00 0.000054

Cold Leg Enthalpy 1266.5 0.052 0.0000 0.262761 0.000047 0.000E+00 0.000047

Reactor Coolant Pump Speed

1485 0.21 0.0000 0.209994 0.000486 0.000E+00 0.000486

Sum of Total Uncertainty, % (Eq 5.8) 0.022

Percentage of Total Uncertainty % (Eq 5.11) 0.305

Average corrected output 2775

Test uncertainty (MW) 8.452

90

APPENDIX 15

DATA ANALYSIS

HIGH T AVG

(403EU)

010MA

AVERAGE

FLUX

020MA

AVERAGE

FLUX

030MA

AVERAGE

FLUX

040MA

AVERAGE

FLUX

2RGL409CA 2RPN413EU 2RPN414EU 2RPN415EU 2RPN416EU

288.6 86.1 86.0 86.1 86.1

0.043 0.327 0.316 0.327 0.324

288.762 87.246 87.070 87.510 87.217

288.501 84.873 85.049 85.137 84.814

0.26 2.37 2.02 2.37 2.40

288.6540 86.1277 86.0268 86.1555 86.1435

0.0347 0.3355 0.3229 0.3261 0.3273

288.7623 87.2461 86.8945 87.3047 87.2168

288.5006 85.2246 85.0488 85.2539 84.9902

288.6260 86.1132 85.9749 86.1095 86.1257

0.0460 0.3308 0.3224 0.3390 0.3239

288.7530 86.8945 86.8945 87.5098 87.0410

288.5100 84.8730 85.0488 85.1367 84.8145

288.6107 86.1139 85.9797 86.1176 86.1224

0.0353 0.3142 0.3003 0.3125 0.3211

288.7249 86.8945 87.0703 87.0117 87.1289

288.5006 85.0781 85.1367 85.1953 84.9609

-0.0082 -0.0109 -0.0382 -0.0324 -0.0149

0.0016 0.0059 0.0221 0.0211 0.0057

0.0069 0.0051 0.0166 0.0117 0.0095

SG1 FEEDWATER

DIFFERENTIAL PRE

SG2

FEEDWATER

DIFFERENTIAL

PRE

SG3

FEEDWATER

DIFFERENTIAL

PRE

SG1

FEEDWATER

TEMP

SG2

FEEDWATER

TEMP

SG3

FEEDWATER

TEMP

SG1 STEAM

PRESS

SG2 STEAM

PRESS

SG3 STEAM

PRESS

SG2

FEEDWATER

PRESS

2ARE051MD 2ARE052MD 2ARE053MD 2ARE005MT 2ARE006MT 2ARE007MT 2VVP017MP 2VVP018MP 2VVP019MP 2ARE003MP

avg 81.77 81.89 78.33 213.1 212.9 213.0 4605.6 4604.7 4616.2 4919.0

stdev 0.945 0.950 0.915 0.009 0.006 0.008 3.735 3.631 3.978 3.657

max 84.484 84.760 81.309 213.099 212.952 213.048 4615.084 4614.392 4625.722 4928.168

min 79.187 78.944 75.462 213.053 212.907 213.002 4591.646 4590.287 4600.242 4905.608

max - min 5.30 5.82 5.85 0.05 0.05 0.05 23.44 24.10 25.48 22.56

Random Uncertainty 0.0556 0.0558 0.0562 0.0002 0.0001 0.0002 0.0039 0.0038 0.0041 0.0036

First 1hr

Ave 81.7594 81.8679 78.3192 213.0792 212.9317 213.0289 4607.3440 4606.4396 4618.0301 4920.7631

StdDev 0.9184 0.9592 0.8986 0.0084 0.0068 0.0088 3.1434 2.9222 3.3101 2.9924

Max 83.9654 84.2865 80.5454 213.0989 212.9523 213.0476 4615.0845 4614.3921 4625.7217 4927.8633

Min 79.1870 78.9443 75.6296 213.0531 212.9295 213.0247 4597.3950 4597.8062 4609.1040 4911.7056

2nd 1hr

Ave 81.7568 81.8709 78.3238 213.0805 212.9308 213.0290 4604.3537 4603.4888 4614.9087 4917.7984

StdDev 0.9533 0.9484 0.9361 0.0096 0.0055 0.0089 4.3018 4.3487 4.6447 4.2604

Max 84.4845 84.0575 81.3088 213.0989 212.9523 213.0476 4615.0845 4612.6230 4624.6138 4928.1680

Min 79.4160 79.0359 75.5991 213.0531 212.9066 213.0247 4591.6460 4590.2871 4600.2417 4905.6084

3rd 1hr

Ave 81.8020 81.9268 78.3545 213.0739 212.9282 213.0245 4605.1147 4604.2565 4615.6894 4918.3192

StdDev 0.9657 0.9416 0.9116 0.0081 0.0052 0.0045 2.9079 2.6832 3.0747 2.7968

Max 84.3623 84.7596 81.0950 213.0989 212.9295 213.0476 4612.2095 4610.8535 4623.7280 4924.8145

Min 79.1870 79.0817 75.4617 213.0531 212.9066 213.0018 4594.9624 4595.8154 4606.6670 4910.1816

Total Ave% change - 1st hr ave 0.0158 0.0246 0.0166 -0.0006 -0.0007 -0.0006 -0.0377 -0.0371 -0.0393 -0.0365

Total Ave % change- 2nd hr ave 0.0190 0.0209 0.0107 -0.0012 -0.0002 -0.0007 0.0273 0.0270 0.0283 0.0238

Total Ave % change- 3rd hr ave -0.0363 -0.0473 -0.0284 0.0019 0.0010 0.0014 0.0107 0.0103 0.0114 0.0132

Std Dev % change - 1st hr Std Dev 2.8594 -0.9962 1.8176 8.4967 -12.5131 -10.1534 15.8415 19.5112 16.7904 18.1710

Std Dev % change- 2nd hr Std Dev -0.8271 0.1378 -2.2736 -4.4509 9.6402 -11.5446 -15.1699 -19.7771 -16.7606 -16.5039

Std Dev% change - 3rd hr Std Dev -2.1391 0.8529 0.3997 11.8293 14.2037 43.3005 22.1486 26.0948 22.7081 23.5183

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APPENDIX 16

RECIRCULATION FACTOR

Coutesy – Glath, J (2012) Primary Plant Performance Functional Specification, Westinghouse

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APPENDIX 17

SHB PROGRAMME USING EXCEL VBA CODE

Figure A17-1: Worksheet showing data imported from KIT

Figure A17-2 Average values from KIT used as SHB Inputs

Figure A17-3: Calculation of feedwater enthalpy using the add-in named “water97-v13”

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Figure A17-4: The VBA code for the feedwater iterative calculation was compiled and used in the

worksheet

Spreadsheet

FigureA17-5: Screen shot of Excel Worksheet containing SHB calculations

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APPENDIX 18

SHB PROGRAMME USING PYTHON CODE

Figure A18-1: The imported files for the various functions

Figure A18-2: The data retrieval from Excel

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Figure A18-3: The calculations for feedwater

Figure A18-4: The outputs into Excel

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APPENDIX 19

PHB PROGRAMME USING EXCEL

Figure A19-1: The data imported to Excel from KIT

Figure A19-2: The Excel Worksheet with the PHB calculations

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